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HANDBOOK  OF 

FIELD  AND  OFFICE  PROBLEMS 
IN  FOREST  MENSURATION 


BY 

HUGO  WINKENWERDER 

Dean,  College  of  Forestn/,  University  of  Washington 

AND 

ELIAS  T.  CLARK 

Associate  Professor  of  Forestry,  University  of  Washington 


SECOND    EDITION 


NEW  YORK 

JOHN  WILEY   &   SONS,  Inc 

London:  CHAPMAN  &  HALL,  Limited 
1922 


Copyright,  1915,  1922,  by 
Hugo  Winkenwerder  and  Elias  T.  Clark 


PRESS    OF 

BRAUNWORTH    &    CO. 

BOOK    MANUFACTUREBO 

BROOKLYN.     N,     V. 


LIBRARY 

N,  C.  State  Colleg 


e 


PREFACE 


The  problems  in  this  handbook  were  originally  prepared  as  an  aid  to  the 
laboratory  instruction  in  forest  mensuration  at  the  University  of  Washington, 
and  were  first  published  by  the  authors  in  1915.  Numerous  changes  and  addi- 
tions were  made  in  this  edition,  particularly  with  reference  to  making  them  more 
generally  useful  to  the  practical  field  and  office  men  and  more  generally  applicable 
to  all  sections  of  the  country.  In  the  few  instances  where  they  are  not  applicable 
they  can  readily  be  made  so  by  slight  modifications  at  the  instance  of  the  instructor 
in  charge. 

In  each  problem  the  forms  for  recording  and  for  working  up  the  data  have 
been  definitely  indicated.  It  has  been  found  that  this  will  result  in  greater 
uniformity  and  better  standards  of  comparison  for  the  work  of  the  individual 
students.  Although  different  schools  are  using  forms  that  differ  in  some  of  the 
details  they  can  readily  be  made  applicable  by  adopting  form  numbers  to  coincide 
with  those  adopted  in  this  handbook.  These  forms  are  illustrated  in  the  Appendix 
on  pages  90  to  97. 

In  the  preparation  of  the  handbook  the  object  has  not  been  to  present  a 
complete  series  of  problems  covering  the  entire  field  of  forest  mensuration,  but 
rather  a  series  of  carefully  selected  type  exercises  which  may  be  used  as  practical 
illustrations  to  supplement  the  recitation  and  text-book  work.  A  number  of  the 
newer  methods  recently  developed  but  not  yet  thoroughly  established  have  been 
purposely  omitted.  References  to  various  new  methods  will  be  found  in  the 
Appendix,  in  connection  with  the  Bibliography.  The  authors  have  included  only 
problems  of  standard  character. 

It  is  hoped  that  the  value  of  the  handbook  will  be  due  as  much  to  what  is 
omitted  as  to  what  is  actually  included.  Ex-perience  has  shown  that  a  few  funda- 
mental type  exercises,  carefully  worked  out  in  the  field  and  laboratory,  and  their 
relation  to  associated  problems  then  brought  out  in  class-room  discussions  will 
give  the  student  a  more  thorough  grounding  in  the  subject  than  a  multitude  of 
exercises  hurriedly  worked  over  but  not  assimilated. 

A  second  feature  sought  in  these  problems  is  the  elimination  of  an  undue 
amount  of  duplication  in  clerical  work.  The  function  of  a  university  is  to  teach 
the  how  and  the  wherefore.  Our  time  is  too  limited  to  use  more  than  a  reasonable 
amount  of  it  for  drill  work,  and  it  has  been  our  experience  that  clerical  drudgery 
often  obscures  the  fundamental  object  of  an  exercise.  Though  a  student  works 
over  only  a  limited  number  of  data  in  the  field  or  laboratory  this  is  no  excuse  for 

iii 

13236 


iv  PREFACE 

an  instructor  to  allow  the  student  to  gain  a  false  impression  concerning  the  actual 
number  of  data  required  in  an  extensive  investigation. 

A  third  object  sought  is  a  thorough  correlation  of  the  individual  fundamental 
problems  in  forest  mensuration  and  to  show  their  relation  to  the  larger  problems 
which  are  usually  dependent  upon  a  combination  of  the  fundamentals.  It  has 
been  sought  to  accomplish  this  by  keeping  the  fundamental  problems  wholly 
distinct  from  each  other  in  the  early  exercises.  This  should  serve  to  prevent 
obscuring  their  broad  field  of  usefulness  for  other  purposes.  In  the  sudceeding 
exercises  the  fundamental  problems  have,  however,  been  combined  with  the 
more  extensive  ones  so  as  to  coordinate  them  and  to  emphasize  their  special  rela- 
tionships. The  directions  for  the  fundamental  problems  are  also  given  in  consid- 
erable detail;  in  the  succeeding  problems,  however,  wherein  the  former  are  used 
only  as  a  step  in  the  solution,  the  student  is  made  to  depend  upon  his  knowledge 
of  the  methods  outlined  in  preceding  problems  by  having  the  directions  in  the 
latter  made  more  general. 

Nearly  all  of  these  problems  have  been  used  in  about  their  present  form  by  the 
students  at  the  University  of  Washington.  Only  such  changes  have  been  made 
as  were  necessary  to  bring  the  manuscript  up  to  date  and  otherwise  put  it  in  proper 
form  for  publication. 

Although  the  majority  of  forest  schools  now  have  their  work  so  arranged 
that  in  connection  with  the  field  work  they  can  obtain  data  for  the  greater  part  of 
the  office  problems,  every  locality  does  not  contain  the  conditions  that  would 
furnish  the  proper  kind  of  data  for  all  of  them.  For  this  reason  data  have  been 
supplied  for  use  in  connection  with  all  of  the  office  problems  presented.  However, 
in  order  to  keep  the  price  of  the  book  within  reasonable  limits  it  has  been  neces- 
sary to  limit  the  quantity  of  these  data  included.  Though  they  are  therefore  not 
adapted  for  extensive  practice  it  is  hoped  they  may  be  of  considerable  help  for 
illustrative  purposes.  Wherever  these  data  are  supplied  in  any  limited  quantity, 
a  special  effort  was  made  to  select  them  with  reference  to  average  conditions  but 
not  so  as  to  destroy  their  general  illustrative  value.  That  the  data  are  only  in  a 
few  cases  presented  on  the  complete  field  forms  should  not  detract  from  their 
value,  but  should  rather  help  the  student  to  remember  just  what  measurements 
are  required  for  a  certain  problem. 

The  authors  wish  to  acknowledge  their  indebtedness  to  Mr.  Bror  L.  Grondal, 
of  the  College  of  Forestry,  University  of  Washington,  and  Mr.  T.  T.  Munger 
and  Mr.  L.  A.  Nelson,  both  of  District  6,  United  States  Forest  Service,  Port- 
land, Oregon,  and  to  the  instructors  in  other  Forest  Schools  who  have  used  the 
"Exercises"  for  helpful  suggestions. 

Hugo  Winkenwerder. 
Eli  AS  T.  Clark. 
University  of  Washington, 
January,  1922. 


TABLE  OF  CONTENTS 


PAGE 

Preface i" 

SECTION  I.     PRELIMINARY  MEASUREMENTS 

PROBLEM 

1.  (Field)    Pacing -  .  .  1 

2.  (Field)    The  Determination  of  the  Diameters  of  Standing  Trees 2 

3.  (Field)    The  Determination  of  the  Heights  of  Standing  Trees 4 

4.  (Office)  The  Construction  of  a  Dendrometer 6 

5.  (Office)  The  Construction  of  a  Hypsometer 6 

6.  (Field)    The  Collection  of  Data  for  Volume  Studies 8 

7.  (Field)   The  Collection  of  Data  for  Growth  Studies 12 


SECTION  II.     USE  OF  GRAPHIC  METHODS 

8.  (Office)  The  Fundamental  Principles  in  the  Use  of  Graphic  Methods . .     15 

SECTION  III.     LOG  RULES 

9.  (Office)  The  Construction  of  a  Scientific  Log  Rule 18 

10.  (Office)  The  Graphic  Comparison  of  Log  Rules 19 

11.  (Office)  The  Extension  of  Log  Rules 19 

SECTION  IV.     PRELIMINARY  CALCULATIONS 

12.  (Office)  The  Determination  of  the  Merchantable  Contents  in  Board 

Feet  of  Felled  Trees 22 

13.  (Office)  The  Determination  of  the  Total  Cubic  Contents  of  Felled 

Trees 23 

14.  (Office)  The  Determination  of  the  Merchantable  Contents  of  Trees  in 

Standards 2o 

15.  (Field)    The  Determination  of  the  Contents  of  Standing  Trees  by 

Short  Methods 25 

y 


vi  TABLE  OF  CONTENTS 


SECTION  V.    THE  CONSTRUCTION  OF  VOLUME  TABLES 

PROBLEM  PAGE 

16.  (Office)  The  Construction  of  a  Merchantable  Volume  Table  in  Board 

Feet  Based  on  D.B.H.  Only 29 

17.  (Office)  The  Construction  of  Full  Stem  Cubic  Foot  Volume  Table 

Based  on  D.B.H.  and  Total  Heights 31 

18.  (Office)  The  Construction  of  a  Table  of  Stem  Form  Factors  Based 

on  D.B.H.  Alone 34 

19.  (Office)  The  Construction  of  a  Merchantable  Volume  Table  in  Board 

Feet  Based  on  D.B.H.  and  Number  of  16-Foot  Logo  by  the 
Frustum  Form  Factor  Method 35 

20.  (Office)  The  Construction  of  a  Taper  Table 37 

SECTION  VI.     SCALING 

21.  (Field)   Scahng  Logs 38 

SECTION  VII.    DETERMINATION  OF  THE  CONTENTS  OF 

STANDS 

22.  (Field)    Obtaining  the   Contents  of   a   Small   Tract  by   Different 

Methods 45 

23.  (Field  and  Office)  Cruising  without  the  Aid  of  a  Volume  Table 47 

24.  (Field  and  Office)  Cruising  with  the  Aid  of  a  Volume  Table ,     51 

SECTION  vilL    GENERAL  GROWTH  STUDIES 

25.  (Field)    The  Determination  of  Total  Ages  of  Trees 57 

26.  (Office)  The  Determination  of  Diameter  Growth  in  Even-aged  Stands  58 

27.  (Office)  The  Determination  of  Growth  in  Uneven-aged  Stands 60 

28.  (Office)  The  Transposing  of  a  Table  of  Diameter  Growth  at  the 

Stump  to  Growth  at  D.B.H 61 

29.  (Office)  The  Determination  of  Height  Growth 62 

30.  (Office)  TheDeterminationof  Volume  Growth  of  an  Individual  Tree..  63 

31.  (Office)  The  Determination  of  Volume  Growth  by  Graves'  Modifica- 

tion of  Mlodjianski's  Method 66 

32.  (Office)  The  Determination  of  Maximum  Growth 68 

SECTION  IX.     SAMPLE  PLOT  STUDIES 

33.  (Field)    The  Determination  of  Contents  of  Stands  by  Means  of  Felled 

Sample  Trees 69 

34.  (Field)    The  Determination  of  the  Rate  of  Growth  in  Even-aged 

Stands  by  the  Analysis  of  Felled  Sample  Trees 72 

35.  (Field)    The  Determination  of  Growth  in  Even-aged  Stands  by  the 

Measurement  of  Standing  Trees 74 


TABLE  OF  CONTENTS  vu 

SECTION  X.     STUDIES  IN  GROWTH  PER  CENT 

PROBLEM  P^«^ 

36.  (Field)    The  Determination  of  Future  Volume  by  Growth  Per  Cent 

Calculated  from  Felled  Sample  Trees 76 

37.  (Field)    The  Determination  of  Future  Volume  in  Immature  Even- 

aged  Stands  by  Gro^\i:h  Per  cent,  Calculated  from  Standing 
Trees "^ 

38.  (Field)    The  Prediction  of  Future  Volume  in  Mature  Stands  from 

Standing  Trees 79 

SECTION  XL     YIELD  TABLE  STUDIES 

39.  (Office)  The  Construction  of  Yield  Tables  for  Even-aged  Stands 80 

40.  (Field)    Method  of  Using  a  Yield  Table  for  Even-aged  Stands 

Uneven-aged  Stands ^^ 


APPENDIX 


PAGE 

Diagram-Correlation  of  Methods  in  Growth  Studies 84 

Explanation  of  Diagram-Growiih  Studies 85 

Bibhograph}' 85 

Units  of  Measurement 89 

Mensuration  Forms 90 

I.  Cross  Section  Sheet 90 

2A.  Analysis  Sheet,  front 91 

2B.  Analysis  Sheet,  back 92 

3A.  D.B.K.  Only,  Cruising  Sheet,  front 93 

3B.  D.B.H.  Only,  Cruising  Sheet,  back 94 

4A.  D.B.H.— Height  Cruising  Sheet,  front 95 

4B.  D.B.H.— Height  Cruising  Sheet,  back 96 

5.     Scaling  Sheet 97 

Columbia  River  Grading  Rules 98 

Puget  Sound  Grading  Rules 99 

Tables 100 

I.  Schiffel  Formula  D.B.H.  Basal  Areas 100 

II.  Schiffel  Formula  Middle  Diameter  Basal  Areas 102 

III.  Basal  Area  of  Circles 103 

IV.  Volumes  of  Frustums  of  Cones 105 

V.  Douglas  Fir  Volume  Table 106 

VI.  Western  Red  Cedar  Volume  Table 107 

VII.  Silver  Fir  Volume  Table 108 

VIII.  Western  Hemlock  Volume  Table 109 

IX.  Scribner  Dec.  C.  Log  Rule 110 

X.  Yield  Table  for  Douglas  Fir 112 

Data  Series 113 

I.  Douglas  Fir  Stem  Measurements 113 

II.  Periodic  Growth  Western  Yellow  Pine 121 

III.  Stump  Analysis,  Second  Growth  Douglas  Fir 122 

IV.  Height  Growth  Data,  Second  Growth  Douglas  Fir 124 

V.  Complete  Stem  Analysis,  Western  Yellow  Pine 125 

VI.  Yield  Table  Data,  Second-Growth  Douglas  Fir 131 

ix 


FIELD   AND   OFFICE   PROBLEMS   IN 
FOREST   MENSURATION 


SECTION  I— PRELIMINARY  MEASUREMENTS 

PROBLEM   1.     (Field.)     Pacing. 

Explanation. — A  great  deal  of  the  work  in  forest  mensuration  requires 
accurate  pacing.  The  student  should  therefore  at  the  outset  learn  to 
establish  a  distance  of  a  surveyor's  chain  or  mile  with  a  fair  degree  of 
accuracy.  In  learning  to  pace  the  student  should  use  his  ordinary  walking 
step.  A  longer  step  may  be  used  with  accuracy  for  short  distances  but 
cannot  be  kept  up  in  long  distance  pacing  without  fatigue. 

Directions. 

A.  Parties. — Each  man  will  do  individual  work  in  this  problem. 

B.  Equipment  Required. 
1  hand  compass. 

1  100-foot  steel  tape. 

1  field  note  book  supplied  with  Form  1. 

C.  Method  of  Procedure. 

1.  With  the  aid  of  another  member  of  the  class  carefully  lay  off  a  quarter 

mile  course  over  fairly  rough  country  with  a  steel  tape  and  a  hand 
compass. 

2.  Go  over  the  course  several  times  using  your  ordinary  step  in  order 

to  determine  how  many  double  paces  you  take  to  cover  the  course. 
Then  adjust  the  number  of  paces  you  take  to  the  quarter  mile  to 
a  certain  even  number  which  can  readily  be  broken  up  into  chains 
and  rods;  i.e.,  240,  250,  260,  etc.  After  establishing  a  standard 
step,  go  over  the  course  repeatedly  until  you  can  cover  the 
distance  with  practically  the  exact  number  of  your  standard  paces. 
You  should  not  be  satisfied  until  your  limit  of  error  is  within 
3  double  paces. 


2  PRELIMINARY   MEASUREMENTS 

Note. — In  practically  all  engineering  and  mensuration  work  the  distance 
between  two  points  is  expressed  in  terms  of  horizontal  distance.  Therefore  in 
pacing  across  broken  country  the  horizontal  distance  must  be  secured.  Where 
the  topography  is  rolling  this  may  be  accomplished  by  slightly  lengthening 
the  step,  but  where  the  slopes  are  steep  resort  should  be  made  to  one  of  the 
following  expedients: 

a.  Take  extra  steps  to  secure  the  unit  pace. 

b.  With  a  Jacob  staff  or  a  stick  lay  off  the  pace  horizontally  on  the  ground. 

c.  Estimate  the    distances  in    terms  of    some  unit  of  distance,   i.e.,     pace 
rod,  or  chain. 

.  When  you  can  pace  the  original  course  satisfactorily,  lay  olT  a  dis- 
tance of  a  quarter  of  a  mile  in  some  other  direction  by  means  of 
pacing  and  a  hand  compass.  During  the  actual  process  of  pacing 
make  a  rough  plat  to  a  suitable  scale  of  the  physical  features  such 
as  woods,  trails,  creeks,  fences,  etc.,  of  the  country  you  cross  and 
note  on  the  plat  the  distance  in  feet  of  each  from  the  starting  point. 
Draw  the  plat  on  Form  1  of  the  Field  Note  Book. 
4.  Check  the  accuracy  of  your  pacing.  With  the  aid  of  another  mem- 
ber of  the  class  go  over  the  course  covered  in  3  above  with  compass 
and  steel  tape  and  note  on  the  plat  the  exact  measured  distances 
from  the  starting  point  to  each  of  the  physical  features  indicated. 

D.  References. — Consult  table  of  units  of  measure  in  Appendi.x. 

PROBLEM  2.    (Field)    The  Determination  of  the  Diameters  of  Standing 
Trees. 
Explanation. — The  object  of  this  exercise  is  to  give  practice  in  estimating 
the  diameters  of  trees  by  eye,  to  show   the   use   of   different   types  of  in- 
struments, and  to  compare  the  efficiency  of  the  different  methods  in  use 

Directions. 

A.  Parties. — Parties  will  consist  of  two  men  each.     The  men  should  alter- 

nate in  the  use  of  the  instruments  and  in  tallying  results. 

B.  Equipynent  Required  per  Party. 
1  pair  tree  calipers. 

1  Biltmore  stick. 

1  diameter  tape. 

1  dendrometer. 

1  field  note  book  supplied  with  Form  1. 

C.  Method  of  Procedure. 

1.  Obtain  the  diameters  at  breast  height  (D.B.H.,  4.5  feet  above  ground) 
in  inches  and  tenths,  of  at  least  20  trees  with  each  of  the  above 
instruments  after  first  estimating  the  diameter  by  eye.  The 
average  diameter  should  always  be  taken  .  This  can  best  be  obtained 
by  taking  two  measurements  at  right  angles  to  each  other. 
In  using  the  instruments  note  the  following: 


DIAMETERS  OF  STANDING   TREES  3 

The  Calipers. — See  that  the  calipers  are  in  adjustment.  If 
•they  are,  the  closed  arms  will  just  fit  together  nicely  when  the 
handles  of  the  arms*  are  pressed  together.  It  they  are  out  of 
adjustment,  adjust  by  means  of  the  set  screw  on  the  movable 
arm.  In  using  the  calipers  he  sure  that  the  movable  arm  is  -pressed 
hack  against  the  scale-beam,  and  that  the  scale-beam  is  placed  against 
the  tree.  This  will  lessen  inaccuracies  due  to  the  arm  being  out  of 
adjustment.  In  calipering  a  large  number  of  trees  care  is  also 
necessary  that  the  measurements  be  taken  at  a  point  4.5  feet 
(D.B.H.)  above  ground. 

The  Biltmore  Stick  is  based  upon  similar  triangles,  and  assumes 
that  the  trees  are  perfectly  round  in  circumference.  To  measure 
a  diameter  with  this  instrument  place  the  stick  flat  against  the  tree 
at  the  point  where  the  diameter  is  to  be  measured,  being  careful 
tha^  it  is  held  horizontal  and  perpendicular  to  the  line  of  sight 
from  the  eye  to  the  center  of  the  tree.  The  eye  should  be  arm's 
length,  25  inches,  from  the  stick.  Move  the  stick  to  right  or 
left  until  the  line  of  sight  from  the  eye  to  the  edge  of  the  tree  passes 
over  the  zero  end  of  the  stick.  The  diameter  is  then  read  where 
the  line  of  sight  to  the  opposite  side  of  the  tree  strikes  the  stick. 
.  In  making  the  reading  be  careful  that  the  head  is  not  moved  and 
that  the  stick  is  not  placed  on  a  ridge  or  in  a  depression  of  the 
bark. 

The  Diameter  Tape. — No  especial  directions  concerning  the 
use  of  the  diameter  tape  should  be  necessary.  If  a  diameter  tape 
is  not  available  use  an  ordinary  tape  graduated  into  feet  and  tenths 
and  divide  by  tt.     Reduce  to  inches  by   multiplying  by   12. 

The  Dendrometer  .—Since  the  types  of  dendrometers  available 
are  so  varied  special  directions  for  using  will  have  to  be  given  by  the 
instructor.  In  this  connection  the  author  has  devised  and  exten- 
sively used  an  instrument  termed  a  "tree  cross"  which  is  based 
upon  the  principle  of  the  Biltmore  stick  except  that  the  scale  is 
attached  by  means  of  a  sliding  and  swiveling  joint  fifteen  inches  from 
the  end  of  a  staff  which  is  sixty  inches  long.  The  measurement  is 
taken  by  placing  the  end  of  the  staff  nearest  the  scale  against  the 
cheek,  the  other  end  against  the  tree  pointing  towards  the  center 
and  reading  the  scale  as  is  done  with  the  Biltmore  stick. 
Tally  the  measurements  of  each  tree  according  to  the  following  form 
of  notes: 

Tree         Ocular         Diameter         Biltmore         Dendrom-  Tree 

No.        estimate  tape  stick  eter  calipers 

When  all  measurements  have  been  taken  on  the  20  trees,  add  up 
the  total  inches  in  each  column;  find  the  difference  between  each 
one  of  these  totals  and  the  total  value  secured  with  the  calipers. 


4  PRELIMINARY   MEASUREMENTS 

Using  the  calipers  as  a  standard  now  fmd  the  ])er('entage  of  error  by 
divifUng  tlie  (HtTerenee  ()l)tained  V)y  the  total  number  of  eaUpered 
inches. 

Comment  on  the  comparative  efhciency  of  the  various  methods 
and  instruments  as  to  accuracy,  portabihty,  etc. 
3.  In  order  to  develop  proficiency  in  estimating  diameters  by  eye  now 
make  an  ocular  estimate  of  a  large  number  of  trees,  checking  each 
estimate  with  the  calipers. 

D.  References.     Numbers  1,  2,  3,  5,  6,  and  10. 

Note. — All   numbers   to   references   in   this   and   succeeding   problems  refer  to 
Bibliography  in  the  Appendix. 

PROBLEM  3.     (Field.)  The  Determination  of  the  Heights  of  Standing 
Trees. 

Explanation. — The  object  of  this  problem  is  to  give  practice  in  estimating 
the  heights  of  standing  trees  by  eye  and  other  rough  methods,  and  by  means 
of  hypsometers,  and  to  compare  the  efficiency  of  the  various  methods. 

Directions. 

A.  Parties. — Students  will  work  in  two-man  parties,  alternating  in  the  use 

of  instruments  and  in  tallying  results. 

B.  Equipment  Required. — All  the  different  types  of  hypsometers  available, 

a  100-foot  tape,  and  notebook  supplied  with  Form  1 . 

C.  Method  of  Procedure. 

1.  Select  a  tree  standing  in  the  open  and  measure  its  height  accurately 

by  means  of  a  transit  or  other  accurate  method  designated  by  the 
instructor.  In  using  the  transit,  set  up  at  any  convenient 
horizontal  distance  measured  from  the  tree,  and  read  the  vertical 
angle  to  the  top  of  the  tree.  With  a  table  of  natural  tangents  of 
a  right  angle  triangle  compute  the  height  of  the  tree  above  the 
level  of  the  center  of  instrument.  In  a  similar  manner  obtain  the 
height  below  this  level  and  add  the  two  for  the  total  height  of  the 
tree. 

2.  Measure   this    tree   by    the   following    rough    methods:  {a)  shadow, 

(6)  two-pole,  (c)  prostrate,  and  {d)  with  single  pole,  and  with 
as  many  of  the  following  hypsometers  as  are  available:  (e)  Klauss- 
ner,  (/)  Faustman,  {(j)  Weisc,  (/?)  Winkler,  {i)  Christen,  (j) 
Brandis,  (A:)  Goulicr,  (/)  omnimeter,  (w)  Abney  level,  (n)  Barbow 
compass,  (o)  Forest  Service  Standard,  (p)  Forest  Service  Compass. 
(See  note  for  description  of  rough  methods.) 


HEIGHTS  0F»  STANDING  TREES  5 

Note. — The  various  rough  methods  are  described  below: 
Sfiadoiv  Method 
(a)   Stick  a  pole  of  any  convenient  length,  upright  in  the  ground  and  measure 

its  heiglit  above  the  ground. 
(6)    Measure   the  shadow  oi   the  pole  and  the  shadow  of  the    tree    and    by 
proportion  compute  the  height  of  the  tree. 

Two-Pole  Method 

(o)   Stick   a  pole  about  4  feet  long,  upright  in  the  ground  at  any  convenient 

distance  from  the  tree. 
(6)    About  6  feet  away  from  this  pole  and  in  line  with  the  first  pole  and     the 

tree  place  a  second  pole  about  10  feet  high. 

(c)  Sight  from  top  of  the  short  pole  and  make  marks  on  the  long  pole  at  the 

intersections  of  the  lines  of  sight  to  the  top  and  to  the  base  of  the 
tree. 

(d)  Measure  the  length  between  these  marks,  the  distance  from  the  top  of 

the  short  pole  to  the  base  of  the  tree  and  the  distance  from  the  top 
of  the  short  pole  to  the  lower  mark  on  the  long  pole. 

(e)  By  proportion  compute  the  height  of  the  tree. 

Prostrate  Method. 
This  method  is  similar  to  the  two-pole  method,  except  that  the  short  pole 
is  dispensed  with  and  the  observer  takes  the  sight  by  lying  on    his  back  on 
the  ground  with  his  foot  against  the  long  pole. 

Sinch-Poh  Method 

(a)  Hold  a  pole  about  5  feet  long  at  arm's  length  loosely  between  the  fingers 
of  one  hand,  so  that  it  will  swing  into  an  upright  position  and  so 
that  the  portion  of  the  pole  above  the  hand  is  equal  in  length  to  the 
distance  of  the  hand  from  the  eye. 

(6)  Without  changing  the  position  of  the  hand  with  reference  to  the  eye, 
step  slowly  forward  or  backward  until  the  line  of  sight  to  the  bas  ,■ 
of  the  tree  strikes  across  the  hand,  and  the  line  of  sight  to  the  top 
of  the  tree  just. includes  the  tip  of  the  pole. 

(e)  The  height  of  the  tree  then  equals  the  distance  of  the  observer  from 
the  tree. 

3.  After  using  the  rough  methods,  use  the  different  hypsometers. 

4.  Tally  all  measurements,  on  Form  1,  according  to  the  following  form  of 
notes: 

Instrument      Total  Error  from  Remarks 

or  m.ethod      Height  Standard 

Two  pole 83  1 

Faustman.  .  .      84  0       0 

The  third  column  will  be  used  for  entering  the  error  of  each  instru- 
ment or  method  from  the  height  as  measured  by  the  transit  or  other 
accurate  method.  The  ''Remarks"  column  will  be  used  for  enter- 
ing the  estimator's  reasons  for  condemning  or  recommending  the 
instrument  or  method. 


6  PRELIMINARY   MEASUREMENTS 

5.  In  order  to  develop  proficiency  in  securing  heights  by  eye  now  estimate 
the  heights  of  a  large  number  of  trees  by  eye.  Check  each  estimate 
with  the  hypsometer  found  to  be  the  best. 

D.  References. — Numbers  4,  8,  10,  11  and  12. 

PROBLEM  4.     (Office)     The  Construction  of  a  Dendrometer. 

Explanation. — The  object  of  this  problem  is  to  illustrate  the  principles  under- 
lying the  construction  of  dendrometers  such  as  the  Biltmore  stick  or  other 
similar  diameter  measures,  and  to  construct  an  instrument  which  can  V)e  used 
in  later  field  problems. 
The  formula  for  securing  the  length  of  graduatioo  of  the  Biltmore  stick  is: 

25D 


V252+25D 
where        a:  =  the  length  of  graduation; 
D  =  the  diameter  of  the  tree ; 

25  =  distance  in  inches  from  the  eye  of  the  observer  to  the  circumference 
of  the  tree. 

Directions. 

A.  Method  of  Procedure. 

1.  Draw  a  diagram  illustrating  the  principle  of  the  Biltmore  stick  de- 

scribed in  Problem  2. 

2.  Work  out  the  complete  algebraic  proof  of  the  formula  given  above  for 

securing  the  length  of  graduation  of  the  stick  in  terms  of  the  25-inch 
distance  and  the  diameter  of  the  tree. 

3.  Compute  the  exact  length  of  graduation  for  each  two-inch  diameter 

class  for  trees  from  ten  to  sixty  inches. 

4.  Select  a  hardwood  stick  approximately  |  inch  scjuare  and  of  a  suitable 

length,  and  bevel  off  one  side.     Upon  this  side  mark  the  graduations 
just  computed, 

B.  References. — Numbers  1,  2  and  3. 

C.  Discussion. 

1.  In  what  respects  would  the  proof  of  the  principle  of  the  tree  cross 

mentioned  in  Problem  2  be  different  from  that  for  the  Biltmore 
stick? 

2.  Give  a  list  of  the  advantages  and  disadvantages  of  the  tree  cross  as 

compared  with  the  Biltmore  stick. 

PROBLEM  5.     (Office)  The  Construction  of  a  Hypsometer. 

Explanation. — The  object  of  this  problem   is  to  illustrate  the  principles 
underlying  the  construction  of  a  hypsometer  such  as  the  Christen  or  the 


THE  CONSTRUCTION  OF  A  HYPSOMETER  7 

Merritt  (Biltmore  Stick)  and  to  construct  an  instrument  which  can  be  used 
in  later  field  problems.     Either  of  the  illustrations  may  be  used. 

Illustration  1. — Construction  of  the  Christen  Hypsometer. 

Explanation. — The  Christen  hypsometer  consists  of  a  flat  piece  of  brass  or 
wood  with  a  notch  near  each  end  between  which  are  placed  graduations 
representing  heights  of  trees.  The  lengths  of  these  graduations  are  secured 
by  the  following  formula : 

AXB 

x  = 

C 

where      .c  =  length  of  graduation,  measured  upward  from  the  lower  notch,  inches; 

A  =  distance  between  notches,  inches ; 

B  =  length  of  the  pole,  feet; 

C  =  height  of  the  tree,  feet. 

In  using  the  instrument  the  observer  holds  the  upper  end  of  the  instru- 
ment suspended  between  his  fingers,  in  front  of  his  eyes  and  at  any  convenient 
distance  away.  An  assistant  holds  upright  against  the  base  of  the  tree  a 
pole  of  the  certain  length  upon  which  the  graduations  of  the  instrument  are 
based.  The  observer  obtains  the  height  of  the  tree  by  moving  towards  or 
from  the  tree  until  it  is  just  included  between  the  notches  and  then  reads 
as  the  height  of  the  tree  the  graduation  intersected  by  the  line  of  sight  to  the 
top  of  the  pole. 
Directions. 

A.  Method  of  Procedure. 

1 .  Draw  a  diagram  illustrating  the  principle  upon  which  the  instrument  is 

based  and  write  out  the  complete  algebraic  proof. 

2.  For  finding  the  length  of  graduations  of  the  instrument  in  terms  of 

the  distance  between  the  notches  of  the  instrument,  the  height  of 
the  tree,  and  the  length  of  the  pole  used  with  the  instrument,  proceed 
as  follows: 
(a)  Using  10  feet  as  the  length  of  the  pole  and  12  inches  as  the  dis- 
tance between  the  notches  of  the  instrument,  work  out  the  length 
of  the  graduation  measured  upw^ard  from  the  bottom  notch  for 
each  five  feet  of  height  for  trees  from  20  to  100  feet  in  height. 
(6)  Shape  a  stick  13X1  X0.25  inches  with  notches  12  inches  apart  and 
to  a  thin  beveled  edge  between  the  notches,  and  mark  the  com- 
puted lengths  of  graduations  on  the  beveled  edge  of  the  stick. 

Illustration  2.* — Construction  of  the  Merritt  Hypsometer. 

Explanation. — Markings  may  be  placed  upon  the  reverse  side  of  the  Biltmore 
stick.  It  should  be  held  upright  in  the  hand  25  inches  from  the  eye  of  an 
observer  when  stationed  1^  chains  from  the  tree. 

♦Note — A  third  type  of  hypsometer  easily  may  be  made  by  attaching  near  one  corner  of  a 
board  ix3^x8  inches,  a  piece  of  wire  which  may  swing  as  a  pendulum.  Graduations  for  tree 
heights  may  then  be  computed  and  marked  along  the  opposite  long  edge  of  the  board. 


8  PRELIMINARY  MEASUREMENTS 

A.  Method  of  Procedure. 

1.  In  a  manner  similar  to  that  explained  above  draw  a  diagram  illustrat- 

ing the  principle  and  work  out  the  formula  for  deriving  the  length 
of  graduations  of  the  Biltmore  stick  when  used  for  securing  the 
16.2-foot  log  lengths  in  standing  trees. 

2.  Compute  the  length  of  graduation  measured  upward  from  the  zero 

end  of  the  Biltmore  stick  for  each  16.2-foot  log  from  one  to  eight. 

3.  Mark  these  graduations  on  the  reverse  side  of  the  Biltmore  stick  con- 

structed in  Problem  4. 

PROBLEM  6.     (Field)  The  Collection  of  Data  for  Volume  Studies. 

Explanation. — The  object  of  this  problem  is  to  illustrate  practically  the 
methods  of  taking  measurements  necessary  for  volume  studies  of  every 
character.  The  student  should  realize  at  the  outset  that  certain  special 
studies  require  only  certain  of  the  measurements  here  called  for  and  that 
when  such  special  studies  are  to  be  made  the  first  step  in  the  work  should  be 
to  determine  just  what  measurements  are  necessary,  so  that  all  unnecessary 
measurements  may  be  eliminated. 

The  organization  of  parties  and  the  routine  as  here  suggested  have  been 
found  efficient  in  Pacific  Coast  timber,  though  it  may  not  prove  so  for  the 
timber  of  other  regions  without  slight  modifications.  Likewise,  when  a 
smaller  variety  of  measurements  is  required,  some  changes  in  this  routme' 
may  be  necessary.  The  proper  key  to  the  situation  has  been  found  only 
when  each  member  of  the  party  is  kept  busy  without  any  "waits,"  for  if  any 
man  has  to  wait  on  any  of  the  others,  the  party  is  not  efficiently  organized. 
The  lengths  in  which  the  sections  will  be  measured  and  the  top  diameter 
limit  to  which  D.O.B.  (diameter  outside  bark)  will  be  taken  will  ordinarily 
depend  upon  the  use  which  is  to  be  made  of  the  data.  If  they  are  to  be  used 
for  the  construction  of  a  rough  "Used  Volume  Table"  showing  the  average 
contents  of  trees  as  utilized  at  a  specific  logging  operation,  measurements 
will  be  taken  to  the  last  saw  cut,  and  the  length  of  sections  will  correspond 
with  the  log  lengths  cut  by  the  logger. 

If  on  the  other  hand  the  data  are  to  be  used  in  the  construction  of  a  general 
volume  table,  a  practically  uniform  volume  should  be  secured  for  all  trees  of 
the  same  size  and  shape.  To  do  this  the  sections  muEt  be  taken  in  regular 
lengths  up  to  a  certain  fixed  diameter  in  the  top,  independent  of  the  variable 
lengths  into  which  different  trees  are  cut  by  the  logger.  In  such  cases  a 
certain  length,  such  as  10.2  feet,  16.2  feet,  or  other  regular  length  with  a 
slight  overlength  above  the  even  foot  to  allow  for  trimming  in  the  mill, 
is  determined  upon  in  advance  of  the  work,  and  trees  are  all  measured  in  this 
length  of  section  up  to  a  certain  fixed  limit  in  the  top,  as  for  example  6,  8  or 
10  inches. 

The  tree  will  then  be  divided  into  sections  of  this  length  up  to  the  fixed 
top  diameter  limit,  regardless  of  whether  the  bole  is  broken  or  defective  or 
of  how  the  tree  has  been  cut  into  logs  by  the  logger.     In  case  the  bole  of  the 


COLLECTION   OF  DATA  FOR  VOLUME  STUDIES  9 

tree  from  the  stuinp-cut  (or  from  a  fixed  height  above  the  ground  should 
the  measurement  of  the  log  sections  not  be  started  from  the  stump)  up  to 
the  top  diameter  limit  does-not  contain  an  even  number  of  regular  sections, 
the  last  section  and  the  fractional  section  will  be  broken  into  two  even-foot 
lengths  of  as  nearly  equal  length  as  possible.  Example:  In  measuring  to 
an  8-inch  top  diameter  limit  with  16.2-foot  sections,  suppose  there  results  a 
section  at  the  top  10.2  feet  long.  Instead  of  taking  the  last  two  sections  in 
these  lengths,  they  should  be  broken  into  a  14.2-foot  length  and  a  12.2-foot 
length  with  the  short  length  at  the  top  and  the  D.O.B.  measurements 
taken  at  the  top  ends  of  these  sections. 

Care  must  be  used  in  selecting  the  trees  for  measurement  in  order  that 
a  range  of  sizes  may  be  obtained  and  in  order  that  only  normal  specimens  are 
.  included.  Abnormal  trees  or  trees  with  any  kind  of  malformation  should 
not  be  measured.  However,  trees  which  are  broken  or  are  defective,  as 
long  as  the  defect  does  not  affect  their  shape,  may  be  taken,  but  they  should 
be  measured  as  entirely  sound  with  no  attention  given  to  the  defect. 

Illustratiox. — To  Collect  Data  for  a  General  Full  Stem  Volume  Study. 

Directions: 

A.  Parties. — The  following  organization  of  the   men  into   3-men  parties, 

with  the  duties  of  each  as  indicated,  will  be  found  efficient:  1.  The 
Notekeeper,  who  is  chief  of  party,  is  responsible  for  all  work,  and  tallies 
all  measurements  called  out  to  him.  2.  The  Caliperman  measures  the 
D.B.H.  and  all  other  diameters  outside  of  bark  with  the  calipers,  and 
the  average  width  of  bark  with  the  analysis  rule.  3.  The  Poleman 
locates  the  D.B.H.  and  measures  the  length  of  all  sections  including 
the  stump  and  tip,  and  the  clear  length. 

B.  Equipment  Required  for  Each  Party. 
1  pair  tree  calipers. 

1  six-inch  flat  boxwood  or  metal  rule  graduated  into  inches  and  tenths. 
1  8-foot  pole,  graduated  into  feet  and  tenths,  and  with  the  D.B.H.  point 

(4.5  feet)  plainly  indicated. 
1  piece  carpenter's  crayon. 
1  belt  axe. 
1  field  notebook  supplied  with  Form  2A. 

C.  Summary  of  Measurements  Required. 

Measurements  Unit  Instrument 

1.  Stump  height Foot  to  nearest  0.1  ft.  8-foot  pole 

2.  Stump  diam.  outside  bark  (D.O.B.) Inch  to  nearest  0.1  in.  Tree  calipers 

3.  Width  of  bark  on  stump Inch  to  nearest  0.1  in.  Boxwood  rule 

4.  D.B.H.  outside  bark Inch  to  nearest  0.1  in.  Calipers 

5.  Length  each  section  and  tip Foot  to  nearest  0.1  ft.  8-foot  pole 

6.  D.O.B.  end  of  each  section Inch  to  nearest  0.1  in.  Calipers 

7.  Width  bark  end  each  .section Inch  to  nearest  0.1  in.  Boxwood  rule 

8.  D.I.B.  end  of  each  section Inch  to  nearest  0.1  in.  (Calculated  by 

notekeeper) 

9.  D.O.B.  at  middle  of  total  height Inch  to  nearest  0.1  in.      Calipers 


10  PRELIMIXARV   MEASUREMENTS 

D.  Method  of  Procedure. 

1.  The  chief  of  party  should  systematize  the  work  as  soon  as  i)ossil)Ic, 

for  not  until  each  man  knows  exactly  what  to  do,  and  follows  the 
same  routine  for  each  tree,  will  the  work  progress  rapidly  and 
efficiently. 

2.  The  following  method  of  procedure  has  been  found  efficient  in  Pacific 

Coast  timber: 

The  Poleman. 

(a)  The  poleman  first  approaches  the  stump  of  a  tree,  marks  it 
with  the  crayon  to  prevent  repetition,  and  then,  setting  the 
8-foot  pole  alongside  it,  obtains  its  height.  Care  must  be 
used  not  to  measure  the  longest  nor  the  shortest  height,  but 
the  average.  The  poleman  then  calls  out  the  measurement  to 
the  notekeeper  and  before  proceeding  further  waits  for  him 
to  repeat  the  figure  to  avoid  errors  in  tallying. 

(6)  Keeping  his  thumb  on  the  pole  at  the  point  which  indicates  the 
height  of  the  stump,  he  lays  the  pole  along  the  first  log  with 
his  thumb  against  the  saw  cut.  The  breast  high  point  on  the 
pole  now  shows  where  the  D.B.H.  measurement  should  be 
taken.  This  point  is  kept  until  the  caliperman  takes  the 
D.B.H.  or  it  is  indicated  by  an  axe  or  crayon  mark. 

(c)  Starting  from  the  saw-cut  at  the  butt  of  the  first  log  the  poleman 
now  proceeds  along  the  bole  (up  the  tree)  measuring  the 
lengths  of  all  sections,  including  the  tip,  and  the  clear  length, 
in  feet  and  tenths.  The  length  of  the  tip  should  be  carefully 
measured  to  the  terminal  bud,  and  if  broken,  a  little  time  and 
care  should  be  used  to  find  the  missing  pieces.  If  they  cannot 
be  found,  however,  the  length  actually  found  should  be 
measured  and  recorded  as  "found  top";  and  the  missing  part 
should  then  be  estimated,  and  recorded  as  "estimated  top" 
on  the  tally  sheet  (analysis  sheet.)  The  clear  length,  which  is 
the  length  from  the  large  end  of  the  butt  log  to  the  first 
prominent  green  limb,  should  be  measured  as  the  poleman 
proceeds  up  the  bole. 

The  Caliperman. 

(a)  The  caliperman  follows  close  behind  the  poleman,  measures  and 
calls  out  to  the  notekeeper  the  various  diameters  and  thickness 
of  bark  measurements  as  they  are  obtained  in  order.  First, 
he  obtains  the  D.B.H.  at  the  point  indicated  by  the  poleman. 
This,  since  it  is  the  most  important  of  all  measurements, 
should  be  obtained  with  great  care  by  taking  the  longest  and 
shortest  diameters,  or,  when  this  is  obviously  impractical, 
by  two  measurements  at  right  angles. 


COLLECTION  OF  DATA   FOR  VOLUME  STUDIES  11 

(b)  Next,  he  measures  the  D.O.B.  at  the  stump,  again  taking  an 

average  of  the  longest  and  shortest  diameters,  and  the  average 
width  of  bark  determined  by  t\^o  or  more  measurements. 
Every  time  he  calls  out  a  measurement  he  should  wait  for 
the  notekeeper  to  repeat  it. 

(c)  In  a  similar  manner  he  proceeds  along  the  bole  and  obtains  the 

D.O.B. ,  and  width  of  bark  at  the  top  end  of  each  section. 
Should  the  sections  not  be  measured  in  the  same  lengths  as 
cut  by  the  logger,  the  width  of  bark  will  have  to  be  secured 
by  chopping  through  it,  taking  care  to  have  the  cut  surface 
perpendicular  at  the  point  where  the  D.O.B.  is  secured. 
Often  when  the  saw  cut  is  not  over  a  few  feet  from  the  point 
where  the  measurement  is  to  be  taken,  or  in  rough  work,  the 
width  of  the  bark  of  the  nearest  saw  cut  may  be  entered  as 
that  of  the  section  being  measured.  A  few  trials  will  readily 
show  to  what  extent  this  is  permissible. 

(d)  The  D.O.B.  at  the  middle  of   the  total  height  of   the  tree  will 

be  measured  in  order  to  compare  the  two  methods  of  com- 
puting volumes  of  trees  explained  in  Problem  13.  It  is  not 
required  in  ordinary  work. 

The  Notekeeper. 

(a)  The  notekeeper  should  always  repeat  the  values  as  they  are 
called  out  to  him  as  a  check  in  tallying  the  measurements. 

(6)  Before  leaving  a  tree  he  should  check  over  his  tally  sheets  to 
ascertain  whether  any  necessary  measurements  have  been 
omitted.  At  odd  moments  he  should  also  make  the  follow- 
ing calculations  and  record  them  in  the  proper  spaces  on  the 
tally  sheet. 

1.  Diameter  inside  bark  at  each  section,  obtained  by  doubling 

the  width  of  bark  and  subtracting  from  the  D.O.B. 

2.  The  total  height,  obtained  by  adding  together  the  length  of 

all  sections,  including  stump  and  tip. 

3.  The  used  length,  which  represents  the  sum  of  the  log  sections 

just  as  used  by  the  logger,  and  hence  does  not  include 
stump  and  tip. 

4.  The  merchantable  length.     This  may  be  the  same  as  the  used 

length  though  not  necessarily.'  It  is  usually  not  when  it 
is  determined  between  a  fixed  diameter  limit  in  the  top, 
irrespective  of  the  sections  as  cut  by  the  logger. 

E.  Discussion. 

1.  Supposing  that  the  field  data  were  to  be  obtained  for  the  construction 
of  a  volume  table  on  the  D.B.H.  only,  and  intended  to  show  the  con- 
tents of  trees  as  cut  by  the  logger,  how  would  the  above  method  of 


12  PRELIMINARY  MEASUREMENTS 

procedure  be  varied  as  to  the  list  of  the  measurements  taken,  the 
organization  of  the  work,  and  the  accuracy  required? 

2.  How  woukl  you  proceed  if  you  were  to  collect  data  in  a  tie  operation 

for  the  construction  of  a  tie  table? 

3.  Give  the  method  of  procedure,  measurements  necessary,  etc.,  for  col- 

lecting data  for  a  cordwood  table. 

4.  In  the  collection  of  volume  table  data,  why  are  broken  or  defective 

sections  of  a  tree  scaled  as  if  sound? 

5.  Why  are  the  measurements  for  a  general  table  usually  taken  in  regular 

length  sections  {i.e.  16.2),  rather  than  in  the  same  lengths  as  cut  by 
the  logger? 

6.  Explain  the  difference  between  fixed,  merchantable,  and  used  limits  for 

the  top  diameters  of  trees  measured . 

7.  How  would  the  organization  of  the  work  in  a  full  stem  volume  study 

be  changed  if  there  were  only  two  men  in  the  party? 

8.  What  is  the  object  of  taking  the  clear  length,  and  when  should  it  be 

omitted? 

PROBLEM  7.     (Field)     The  Collection  of  Data  for  Growth  Studies. 

Explanation. — The  illustration  given  below  aims  to  include  all  measurements 
required  in  any  growth  study  concerning  itself  with  the  stem  of  the  tree 
(hence  it  does  not  include  branches),  and  unless  a  specific  problem  involves  a 
full  stem  analysis  all  of  the  measurements  enumerated  below  may  not  be 
required.  As  in  Problem  6,  the  student  should  realize  that  the  first  important 
step  in  the  collection  of  data  for  any  specific  problem  will  be  to  determine 
just  what  measurements  are  required. 

Illustration. — To  make  a  Complete  Stem  Analysis, 

Directions. 

A.  Parties. — The  organization  of  men  into  parties  will  be  the  same  as  for 

Problem  6,  except  that  the  taking  of  the  D.B.H.  and  the  D.I.B. 
measurements  of  each  section  will  be  added  to  the  duties  of  the  pole- 
man;  and  the  caliperman  now  becomes  the  ring  counter.  The  duties 
of  the  latter  will  be  to  count  the  rings  at  each  cut,  to  make  the  decade 
measurements,  and  to  obtain  the  thickness  of  bark. 

B.  Equipment  Required  for  Each  Parti/. — Same  as  for  Problem  6,  with  the 

addition  of  a  small  hand  magnifying  glass  to  aid  in  counting  the  annual 
rings  and  an  analysis  or  similar  rule  graduated  into  inches  and  twen- 
tieths. If  the  trees  are  more  than  2 1  inch(>s  in  diameter  inside  the  bark 
at  the  stump,  the  analysis  rule  should  be  24  inches  long.  It  will  also 
be  found  a  great  aid  to  the  work  if  this  is  sui)plied  with  a  centering  point 
attached  at  the  zero  mark . 


COLLECTION   OF  DATA  FOR  GROWTH   STUDIES 


13 


C.  Measurements  Required  .—The  measurements  will  correspond  to  those 
outlined  for  Problem  6,  except  that  the  D.I.B.  at  the  top  end  of  each 
section  will  be  taken  instead  of  the  D.O.B.  The  following  additional 
measurements  will  also  be  necessary: 


Measurements 

Unit 

Instrument 

Total  age 

Years 

To  be  determined  by  a  sepa- 
rate  special  study  on  seed- 
lings; see  Problem  25 

Age  at  each  cross-cut 

Years 

Hand  lens 

Measurements  taken  on  average  radius  in  ten- 

Inches  to 

Analysis  rule 

year  periods  (decades) 

nearest 
0.05 

D.  Method  of  Procedure. 

1.  The  Poleman. 

The  Poleman,  with  the  added  duties  of  caliperman,  will  follow  the 
same  routine  as  before  (see  Problem  6),  except  that  both  series  of 
measurements  will  be  made  at  the  same  time  as  he  proceeds  along 
the  tree. 

2.  The  Ring  Counter. 


(a) 


(c) 


id) 


The  Ring  Counter  first  obtains  the  average  width  of  the  bark. 

Then  with  the  D.I.B.  as  obtained  by  the  poleman  he  computes 
the  average  radius,  and  with  the  centering  pin  at  the  pith  of  the 
tree  he  swings  the  analysis  rule  until  the  length  of  the  average 
radius  just  cuts  the  outer  edge  of  the  last  ring. 

A  straight  line  is  now  drawn  from  the  pith  to  the  bark  along  this 
radius.  The  rings  are  then  counted  from  the  bark  to  the  pith 
and  the  tenth  ring  of  each  decade  marked  with  a  soft  pencil. 
Care  should  be  used  to  place  the  mark  within  the  tenth  ring. 

The  total  age  at  the  cut  and  the  distances  from  the  pith  to  each 
tenth  ring  are  then  read  off  to  the  note-keeper  m  inches  to  the 
nearest  0.05.  In  reading  off  the  decade  measurements  care 
should  be  taken  to  read  to  the  inner  edge  of  the  early  wood  of 
each  of  the  marked  rings. 

3.  The  Tallyman. 

(a)  The  Tallyman  records  the  measurements  in  the  proper  column  on 
the  Tree  Analysis  Blank  (Form  2A  and  B.)  In  recording  the 
first  decade  measurement  it  will  be  found  that  it  usually  does 
not  represent  a  full  period  of  ten  years.  The  number  of  rings 
included  in  this  measurement  should  therefore  be  indicated  in 
the  upper  left-hand  corner  of  the  space  allotted  to  this  measure- 
ment on  the  back  side  of  the  sheet  (Form  2B.),  and  divided  off 
from  this  space  by  a  diagonal  line. 

(6)  He  should  make  the  following  checks  on  the  analysis  sheet. 


14  PRELIMINARY   MEASUREMENTS 

1.  The  last  decade  measurement  should  equal  one-half  the  D.I.B. 

as  previously  tallied. 

2.  The  age  at  any  cut  should  be  equal  to  the  total  number  of 

decades  minus  one,  times  10,  plus  the  number  of  rings  recorded 
in  the  upper  left-hand  corner  of  the  space  allotted  to  the  first 
decade  measurement. 

3.  The  consecutive  cross-sections  should  show  a  decrease  in  age 

from  stump  to  tip. 

4.  Before  leaving  the  tree  he  should  carefully  check  over  the  entire 

tally  sheet  to  see  that  none  of  the  necessary  measurements 

have  been  omitted, 
(c)   In  making  the  necessary  calculations  he  determbies  the  D.O.B. 
at  each  cut  instead  of  the  D.I.B.  as  was  done  in  Problem  6. 
This  is  done  by  adding  twice  the  thickness  of  the  bark  to  the 
recorded  D.I.B. 

E.  References. — Numbers  7,  9  and  80. 


SECTION  II— USE  OF  GRAPHIC  METHODS 

PROBLEM    8.     (Office.)     The    Fundamental    Principles    in    the    Use    of 
Graphic  Methods. 

Explanation. — In  this  problem  one  of  the  simplest  problems  involving  the 
plotting  of  curves  has  been  chosen  and  outlined  primarily  with  reference  to 
illustrating  the  fundamental  principles  of  determining  averages  by  means  of 
plotted  values,  and  to  show  something  of  the  significance  of  bringing  out  a 
series  of  related  results  by  graphic  representation. 

Illustration. — To  Make  a  Table  of  Average  Heights  on  Diameters  by  Plot- 
ting the  Values  on  Co-ordinate  Paper. 

Directions  : 

A.  Data  Required. — Measurements  showing  the  total  heights  of  trees  of  dif- 

ferent diameters  at  breast  height.     Use  Data  Series  I  in  the  Appendix. 

B.  Method  of  Procedure. 

(a)  Preparing  the  Co-ordinate  Paper. 

1.  The  problem  used  to  illustrate  this  exercise  aims  to  determine  an 

average  height  for  certain  specified  diameters,  i.e.,  the  diameters 
of  the  trees  are  independent  variable  quantities  and  the  heights 
dependent  variables.  As  it  is  customary  to  let  abscissae  on  the 
cross-section  paper  represent  the  independent  values  and 
ordinates  the  dependent  values,  in  this  problem  let  the  abscissa? 
represent  diameters  and  the  ordinates  heights.  It  is  a  rule 
to  let  horizontal  distances  from  the  vertical  axis  represent 
abscissae,  and  vertical  distances  from  the  longitudinal  axis 
ordinates. 

2.  Having  determined  which  values  shall  be  represented  by  abscissae 

and  which  by  ordinates,  the  next  step  is  to  determine  the  limits 
of  variation  which  the  data  will  represent  {i.e.,  in  this  problem, 
what  are  the  smallest  and  the  largest  values  for  diameters  and 
for  heights  that  it  will  be  necessary  to  plot?),  so  that  the  unit 
best  adapted  for  each  of  the  co-ordinate  axes  can  be  decided 
upon.  In  deciding  this  unit,  remember  that  the  larger  the  unit 
the  more  accurate  will  be  the  results  (so  that  the  entire  sheet 
of  paper  should  be  utilized  as  far  as  practicable),  and  also  that 
15 


16  USE  OF   GRAPHIC    METHODS 

the  general  aim  should  he  io  choose  such  unils  (hot  (lie  curve  loill 
be  neither  very  Jlat  nor  very  sleep.  This  aim  is  (icconiplished  if 
the  largest  ordinate  is  not  more  than  one  and  one- half  times  the 
largest  abscissa.     Remember  this  in  connection  with  all  curves. 

3.  Having  determined  the  units  for  ordinates  and  abscissae,  starting 

from  the  lower  left-hand  corner  of  the  page  lay  off  and  mark 
the  respective  values  on  each  axis.  Always  label  these  carefully 
along  the  edge  of  the  paper;  i.e.,  "Diameters  in  Inches," 
"Heights  in  Feet,"  etc. 

4.  In  plotting  the  values  remember,  as  before  stated,  that  the  hori- 

zontal distances  from  the  vertical  axis  represent  the  values  of 
the  abscisstr.  (diameter  values  in  this  case),  and  that  the  ver- 
tical distances  from  the  horizontal  axis  represent  the  ordinates 
(heights  in  this  case.) 

The  two  variable  quantities,  the  height  for  a  specified  diam- 
eter, can  be  expressed  by  a  single  point  on  the  co-ordinate  paper ; 
namely,  that  point  at  which  the  perpendicular  lines  extending 
from  the  respective  abscissa  and  ordinate  axes  cross.  After 
the  location  of  the  first  point  has  been  determined  plot  the 
values  of  all  other  trees  in  the  data  supplied.  Where  a  second 
point  occurs  at  the  intersection  of  the  same  lines  place  a  small 
figure  "2"  beside  the  point  already  plotted,  for  a  third  point 
of  the  same  value  a  small  figure  "3,"  and  so  on. 

(6)   Averaging  the  Values. 

5.  When  plotting  is  completed,  the  next  step  is  to  average  the  values 

in  accordance  with  the  object  sought.  In  this  problem  the 
average  height  will  be  determined  for  each  2-inch  diameter 
class  in  even  inches.  Remember  that  in  all  of  these  problems 
two  sets  of  averages  must  be  obtained.  In  this  problem  we 
have  (1)  the  average  heights  for  the  diameter  classes  and  (2) 
the  average  diameter  of  each  diameter  class.  Let  each  of  the 
diameter  classes  begin  with  the  fractional  part  of  the  preceding 
whole  odd  inch  and  end  with  the  next  succeeding  whole  odd  inch, 
of  the  diameter  class,  i.e.,  5.1  inches  to  7.0  inches  inclusive  will 
comprise  the  6-inch  class.  In  1-inch  classes  it  should  be  from 
5.6  inches  to  6.5  inches  inclusive.  The  average  abscissa  for  each 
diameter  class  will  be  found  by  adding  horizontally  the  values  of 
all  points  plotted  within  each  diameter  class,  and  dividing  by  the 
total  number  of  points.  Similarly  the  average  ordinate  for  each 
diameter  class  will  be  found  by  adding  vertically  the  values  of  the 
same  points,  and  dividing  by  the  number  of  points.  With  these 
two  average  values  at  hand  now  plot  the  average  point  in  its 
proper  place  as  was  done  with  the  points  for  the  individual  trees. 
In  order  that  this  point  may  be  distinguished  from  the  others 


FUNDAMENTAL  PRINCIPLES  17 

enclose  it  within  a  small  circle  or  square.  Opposite  the  average 
point  enter  the  number  of  trees  that  the  point  represents. 

Note. — The  following  short  cut  in  averaging  saves  a  great  deal  of  time.  Instead  of  adding 
the  actual  values  represented  by  the  plotted  points,  let  the  first  heavy  line  below  and  a  similar 
one  to  the  left  of  the  group  of  points  to  be  averaged  represent  zero  lines.  Now  find  the  value 
of  each  point  in  terms  of  the  number  of  spaces  it  is  located  from  the  new  zero.  Average, 
and  locate  the  new  point  accordingly. 

(c)    Draicing  the  Curve. 

6.  Connect  the  average  points  by  fine  straight  hncs.     This  will  help 

to  show  the  general  direction  of  the  curve. 

7.  Next  locate  the  direction  of  the  curve  by  eye.     In  doing  this 

imagine  the  curve  as  a  flexible  steel  band  so  placed  that  the  aver- 
age points,  which  are  considered  as  magnets  of  a  strength 
dependent  on  the  number  of  trees  represented,  are  about  equally 
located  on  either  side  of  it.  The  band  will  then  take  a  position 
nearest  the  points  with  the  greatest  attractive  force.  After 
locating  the  direction  of  the  curve  by  the  eye,  sketch  in  it  free- 
handed as  smoothly  and  regularly  as  possible,  and  finally  smooth 
off  the  irregularities  by  means  of  a  spline  or  adjustable  curve. 

8.  From  this  curve  construct  a  table  of  heights  for  each  diameter  in 

whole  inches  by  noting  the  points  where  the  respective  perpen- 
dicular lines  from  the  co-ordinate  axes  meet  the  curve. 

C.  Discussion. 

1.  Supposing  that  the  method  of  first  averaging  and  then  plotting  the 

averaged  points  were  used  instead  of  that  described  above,  explain 
in  detail  how  the  method  of  proced\ire  would  be  varied. 

2.  Why  can  not  the  data  be  averaged  in  the  above  problem  just  as  well 

without  plotting  values  and  drawing  a  curve? 


SECTION  III— LOG  RULES 
PROBLEM  9.     (Office.)     The  Construction  of  a  Scientific  Log  Ruls. 

Explanation. — The  object  of  this  problem  is  to  illustrate  the  fundamental 
principles  underlying  the  determination  of  the  contents  of  logs  in  board 
measure.  A  thorough  preliminary  study  of  a  rule  such  as  the  International, 
which  is  constructed  upon  scientific  principles,  should  give  the  student  a 
thorough  understanding  of  the  determination  of  the  contents  of  logs  in  board 
feet,  and  a  scientific  foundation  upon  which  to  base  his  general  study  of  log 
rules. 

Illustration. — The  International  Log  Rule. 

The  formula  for  securing  the  volume  of  a  log  4  feet  in  length  by  the 
International  log  rule  is 

F  =  0.22D2-0.71D, 
where  V  =  the  volume  of  the  log  in  feet  B.M . ; 

D  =  the  diameter  in  inches  at  the  top  end  of  the  log. 

This  formula  is  based  upon  the  assumption  of  a  loss  for  each  1  inch  board 
of  i-inch  in  saw  kerf,  and  ye  inch  for  shrinkage  and  that  the  loss  in  slabbing, 
edging  and  surface  waste  is  equivalent  to  a  board  2.12  inches  thick,  of  the 
same  width  as  the  diameter  of  the  log  and  the  same  length  as  the  length  of 
the  log. 

Directions: 

A.  Methods  of  Procedure. 

1.  Work  out  the  complete  algebraic  proof  of  the  International  rule  for 

4-foot  lengths,  noting  the  reason  for  each  step. 

2.  Using  the  formula  for  4-foot  lengths,  and  allowing  ^-inch  taper  for  each 

4  feet,  compute  the  volumes  of  the  logs  of  all  diameters  from  6  inches 
to  16  inches  inclusive,  and  each  length  in  even  4-foot  lengths  from 
8  feet  to  24  feet  {i.e.,  8-,  12-,  16-,  20-  and  24-foot  lengths) .  Arrange 
the  results  in  table  form  leaving  blank  spaces  for  the  alternating 
even-foot  lengths  (i.e.,  10-,  14-,  IS-,  and  22-foot  lengths.) 

3.  Now  determine  the  values  for  the  missing  alternating  lengths  by  plot- 

ting a  separate  curve  for  each  diainc^tor  from  6  inches  to  12  inches 
using  abscissa)  as  lengths,  and  ordinates  as  volumes. 
IS 


THE  GRAPHIC  COMPARISON   OF   LOG   RULES  19 

4.  From  these  curves  read  off  the  vohimes  for  the  missing  lengths,  and 

enter  in  the  table. 

5.  Take  a  smooth  stick-0.5XlXl3  inches  and  enter  on  it  the  values  in 

the  table, in  the  same  manner  as  they  occur  on  the  ordinary  scale 
stick. 

B.  References.     Numbers  17,  18,  25,  26,  and  27. 

C.  Discussion. 

1.  Write  brief  directions  for  using  the  scale  stick  in  scaling  logs. 

2.  What  is  the  object  in  drawing  the  curve  in  this  problem? 

3.  What  particular  fundamental  principles  make  the  International  Rule 

more  accurate  than  other  formula  rules  such  as  the  Doyle. 

4.  What  advantages  has  a  formula  rule  over  a  diagram  rule? 

PROBLEM  10.     (Office.)     The  Graphic  Comparison  of  Log  Rules. 

Explanation. — To  illustrate  the  extreme  variations  in  values  obtained  by 

scaling  with  different  log  rules. 
Illustration. — The  International,  Scribner,  and  Doyle  Rules. 

Directions  : 

A.  Method  of  Procedure. 

1.  On  a  sheet  of  co-ordinate  paper  lay  off  diameters  in  inches  as  abscissa 

on  the  long  edge  of  the  sheet,  and  volumes  in  board  feet  as  ordinates. 
Be  sure  first  to  determine  the  number  of  spaces  you  will  allow  to 
each  unit  by  an  examination  of  the  data  to  be  plotted. 

2.  With  values  read  from  a  scale  stick,  or  from  the  respective  tables  in 

Graves'  Mensuration  or  the  Woodsman's  Handbook,  Bull.  36  U.  S. 
Dept.  of  Agr.,  construct  on  the  same  sheet  of  cross-section  paper 
curves  representing  the  values  of  the  16-foot  logs  of  all  diameters 
given  by  the  International,  the  Scribner,  and  the  Doyle  Rules. 

B.  References.     Numbers  16,  19,  20,  23  and  24. 

C.  Discussion. 

1.  Comment  on  the  relationships  as  illustrated  by  the  curves. 

2.  Could  a  combination  table  for  the  " Doyle-Scribner "  Rule  be  con- 

structed so  as  to  yield  low  values? 

PROBLEM  11.     (Office.)     The  Extension  of  Log  Rules. 

Explanation. — The  object  of  this  problem  is  to  show  how  log  rules  with  values 
reading  only  to  a  certain  point  may  be  extended  so  that  the  rule  may  be 
applied  to  logs  of  other  dimensions.  The  method  of  procedure  here  outlined 
for  log  rules  may  also  be  used  in  the  extension  of  volume,  growth,  or  any  other 


20 


LOG    RULES 


tables  in  which  the  values  vary  more  or  less  regularly  according  to  some 

definite  law. 
Illustration  1. — Extension  by  prolonging  a  curve. 
Explanation. — The  Drew  Rule  has  been  chosen  for  this  illustration  because 

it  gives  values  only  for  logs  above  20  feet  in  length.     The  object  will  be  to 

extend  the  values  for  16-inch  logs  so  that  they  may  be  scaled  down  to  10-foot 

lengths. 

Directions  : 

A.  Method  of  Procedure. 

1.  With  lengths  in  feet  as  abscissae  and  volumes  in  board  feet  as  ordinates, 
plot  the  following  values  for  16-inch  logs  by  the  Drew  Rule. 


Length, 

Volume, 

Length, 

Volume, 

Feet 

B.M. 

Feet 

B.M. 

20 

194 

32 

311 

22 

214 

34 

330 

24 

233 

36 

350 

26 

252 

38 

369 

28 

272 

40 

388 

30 

291 

2.  Extend  the  curve  backward  to  10  feet.     Be  careful  that  the  extended 

portion  of  the  curve  follows  the  spme  general  trend  as  the  original 
curve. 

3.  Read  values  from  the  curve  for  lengths  from  20  feet  down  to  10  feet 

in  2-foot  classes  and  tabulate. 

4.  The  values  for  other  inch  classes  may  be  extended  backward  in  a  sim- 

ilar manner,  and  the  values  thus  secured  tabulated. 
Illustration  2. — Extension  by  interpolation. 

Explanation. — The  Vermont  Rule  gives  the  following  board  foot  contents 
for  16-foot  logs. 


Diameter, 

Volume, 

Diameter, 

Volume, 

Inches 

B.M. 

Inches 

B.M. 

G 

24 

16 

170 

8 

43 

18 

217 

10 

66 

20 

267 

12 

96 

22 

320 

14 

130 

24 

384 

The  object  will  be  to  extend  this  rule  so  that  volumes  for  logs  "d  to  36 
inches  in  diameter  can  be  obtained. 


THE  EXTENSION   OF   LOG   RULES  21 

Directions  : 

A.  Method  of  Procedure. 

1.  Find    the  difference  in  volume  between  the  diameters  of  14  and  16 

inches,  16  and  18  inches,  18  and  20  inches,  20  and  22  inches,  22  and 
24  inches. 

2.  Find  the  average  of  these  differences. 

3.  Find  the  average  increase  of  these  differences. 

4.  To  the  vahie  of  a  24-ifich  log  as  given  in  the  table  add  the  average 

difference  found  in  2,  plus  the  average  increase  found  in  3  and  the 
volume  of  a  26-inch  log  will  be  obtained. 

5.  Secure  the  volume  of  a  28-inch  log  similarly  by  adding  to  the  value  of 

a  26-inch  log  the  average  difference  plus  twice  the  average  increase. 

6.  Continue  this  operation  for  all  even  diameters  up  to  36  inches  and 

tabulate. 

7.  The  values  for  other  log  lengths  may  be  extended  in  a  similar  manner 

and  the  values  thus  secured  tabulated. 

B.  References.     Number  21. 

C.  Discussion. 

1  From  this  problem  and  the  preceding  one  would  you  say  that  there  is 
ever  any  justification  for  extending  a  log  rule  by  tacking  one  rule 
onto  another? 

2.  What  are  the  different  uses  of  plotted  curves  as  illustrated  in  Prob- 
lems 8,  9,  10  and  11. 


SECTION   IV— PRELIMINARY  CALCULATIONS 

Explanation. — The  object  of  this  section  is  to  give  the  student  sufficient 
practice  in  making  calculations  by  means  of  the  various  units  used  in  forest 
mensuration,  so  that  such  calculations  may  be  largely  dispensed  with  in  suc- 
ceeding problems  wherein  they  become  merely  clerical  work. 

PROBLEM   12.     (Office.)     The   Determination  op  the  Merchantable  Con- 
tents IN  Board  Feet  of  Felled  Trees. 

Directions  : 

A.  Data  Required. — Use  the  tree  measurement  data  collected  in  Problem  6. 

B.  Method  of  Procedure. 

1,  With  the  aid  of  a  Scribner  decimal  C  log  table  or  scale  stick  determine 
the  volume  in  board  feet  of  each  log  section  measured  except  stump 
and  tip,  as  shown  by  the  length  of  the  section  (log)  and  the  diameter 
inside  of  bark  at  the  small  end  of  the  section.  Round  off  all  diam- 
eters to  the  nearest  whole  inch  above  or  below  the  actual 
diameter.  In  rounding  off  diameters  classify  logs  with  diam- 
eters exactly  half-way  between  inches  (0.5  inch)  in  the  next 
lower  inch.  Place  all  lengths  in  the  even  2-foot  length  next 
below  the  actual  size,  unless  "penalty  scaling"  is  practised  in  which 
case  place  logs  which  exceed  a  certain  amount  allowed  for  trimming 
in  the  sawmill,  in  the  next  higher  even-foot  length.  Enter  the 
volumes  in  the  proper  columns  on  the  analysis  blank.  (Form  2A.) 
Since  in  the  construction  of  the  Scribner  decimal  C  rule  the  end 
figure  is  dropped,  add  a  cipher  to  the  volume  of  each  section  as  read 
from  the  table  to  secure  the  full  scale  of  the  log  to  the  nearest  10  feet. 

Note. — Where  the  Scribner  decimal  C.  rule  is  used  for  scaling  Pacific  Coast  timber,  the 
maximum  scaling  length  of  any  section  should  not  exceed  32  feet;  i.e.,  logs  up  to  and  including 
82  feet  in  length  should  be  scaled  as  one  log,  and  logs  longer  than  this  as  two  logs  of  as 
nearly  equal  even-foot  lengths  as  possible,  the  shorter  length  to  be  taken  nearer  the 
smaller  diameter.  In  this  case  the  diameter  at  the  end  of  the  larger  log  will  be  determined  in 
Pacific  Coast  species  by  allowing  one  inch  increase  for  every  10  feet  of  length  for  taper; 
i.e.,  for  lengths  from  5  to  15  feet  allow  1  inch,  for  lengths  from  16  to  25  feet  2  inches.  To 
illustrate  further,  a  36-foot  log  should  be  broken  into  two  18-foot  sections,  and  the  diameter 
at  the  end  of  the  butt  section  as  2  inches  larger  than  the  top  diameter  at  the  small  end  of 
the  whole  (36-foot)  log.  Similarly,  a  38-foot  log  would  be  broken  into  a  20-foot  section  and 
an  18-foot  section,  the  longer  section  at  the  butt  end  with  a  diameter  2  inches  larger  than 
the  top  section. 

22 


.  TOTAL  CUBIC  CONTENTS  OF  FELLED  TREES  23 

2.  Add  the  volumes  of  all  sections  to  determine  the  total  merchantable 
volume  of  the  entire  tree,  and  record  in  proper  space. 

C.  References.     Number  45. 

PROBLEM  13.     (Office.)     The  Determination  of  the  Total  Cubic  Contents 
OF  Felled  Trees. 

Explanation. — The  object  of  this  problem  is  to  show  the  comparative  value 
of  the  different  methods  and  to  develop  proficiency  in  making  the  various 
fundamental  calculations  required  in  the  determination  of  the  cubic  contents 
of  trees. 

Illustration  I. — To  compute  the  cubic  contents  of  felled  trees  by  cubing  the 
tree  in  sections. 

Explanation. — In  this  method  each  section  in  the  tree  is  compared  to  a 
geometric  figure  and  for  that  reason  logs,  stumps,  tips  and  branches  each 
require  the  use  of  a  distinct  formula .     The  various  formulae  follow : 

A.  The  Cubic  Contents  of  Logs. 

1 .  Let  B  =  basal  area  in  square  feet  of  large  end  of  log ; 

6  =  basal  area  in  square  feet  of  small  end  of  log; 
L  =  length  of  log. 

Then  the  cubic  contents  may  be  expressed  by  Smalian's  formula  as 
follows : 

2.  Determine  basal  areas  in  square  feet  by, — 

4   ^144' 

Where  d  =  the  diameter  of  the  area  in  inches  and  —  is  used  to 

144 

reduce  to  square  feet. 

B.  The  Cubic  Contents  of  Stumps. 

A  stump  is  treated  as  a  cylinder  whose  diameter  is  equal  to  the  top 
diameter  of  the  stump.     The  formula  for  the  cylinder  is 

BXL. 

C.  The  Cubic  Contents  of  Tips. 

A  tip  is  treated  as  a  cone  whose  basal  area  is  equal  to  the  basal  area  of 
the  tip,  and  whose  altitude  is  equal  to  the  length  of  the  tip.  The  formula 
is, 

\BXL. 


M  f   State  College 


24      «'•    *"  PRELIMINARY   CALCULATIONS 

D.  The  Cubic  Contents  of  Branches. 

A  branch  is  treated  as  a  cylinder  whose  diameter  is  equal  to  the  diam- 
eter of  the  middle  of  the  branch.  Letting  Bi  equal  the  middle  diameter 
and  L  the  length,  the  formula  becomes, 

BiXL. 

Directions. 

A.  Data  Required. — Use  the  data  collected  in  Problem  6. 

B.  Method  of  Procedure. 

1.  Compute  the  contents  of  one  tree  according  to  the  formula)  given  in 

the  Explanation. 

2.  In  the  remaining  data  use,  in  place  of  the  formula  for  basal  areas,  the 

table  of  basal  areas  given  in  the  Appendix  (Table  IIL). 

3.  Tally  all  volumes  in  the  proper  column  on  the  analysis  blank  and  total. 
Illustration  2. — To  Compute  the  Cubic  Contents  of  Felled  Trees  by  Cubing 

the  Tree  as  a  Whole  (Schiffel  Method). 
Explanation. — The  following  formula  for  securing  the  full  stem  volumes  of 
trees,  devised  by  Professor  Schiffel  of  the  Austrian  Experiment  Station,  has 
recently  been  introduced  in  this  country. 

Cubic  contents  of  a  tree  =  (0.16  B-\-O.QQb)H, 

where  J5=area  in  square  feet  at  the  D.B.H.  point; 

h  =  basal  area  in  square  feet  at  the  middle  of  the  total  height ; 
H  =  total  height  in  feet. 

This  formula  is  explained  in  the  ''Centralblatt  fiir  das  gesamte  Forst- 
wesen"  for  December,  1906.  It  has  not  yet  gained  general  use  in  the  United 
States  as  its  accuracy  has  not  been  completely  established.  This  illustra- 
tion serves  to  compare  its  accuracy  with  the  SmaUan  method  of  cubing  trees. 

Directions. 

A.  Data  Required. — Use  the  same  data  as  in  Illustration  1. 

B.  Method  of  Procedure. 

1.  Compute  the  cubic  volume  of  one  tree  using  the  Schiffel  formula. 

2.  In  the  remaining  data  use  tables  Number  I  and  II  in  the  Appendix 

for  finding  value  of  0.16  B  and  0.66  b. 

C.  References. — Numbers  28,  29  and  31. 

D.  Discussion. 

1.  Comment  on  the  relative  accuracy  of  this  method  as  compared  with 
that  of  cubing  each  section  separately  outlined  in  Illustration  I. 


CONTENTS  OF  TREES  IN  STANDARDS  25 

2.  In  what  way  will  tlii's  method  decroase  the  necessary  field  work  involved 
in  securing  the  tree  measurements? 

PROBLEM  14.     (Office.)     The  Detek.mi.xatiun  of  the  Merchantable  Contents 
OF  Trees  in  Standards. 

Explanation. — A  Standard  is  a  log  of  specified  dimensions  used  as  a  unit  of 
volume.  It  is  based  on  the  principle  that  the  contents  of  logs  vary  directly 
as  their  lengths  and  the  squares  of  their  respective  diameters.  The  volume  of 
any  log  in  terms  of  a  specified  standard  may  be  obtained  as  follows : 

''Square  the  diameter  at  the  small  end,  and  divide  by  the  square  of  the 
diameter  of  the  standard  log;  then  divide  by  the  length  of  the  standard  log 
and  multiply  by  the  length  of  the  log  measured." 

Illustration. — To  compute  the  Merchantable  Contents  of  Trees  in  the  "  19- 
inch  Standard." 

Explanation. — The  "19-inch  Standard"  is  a  log  13  feet  long  and  19  inches 
in  diameter  at  the  small  end.  The  formula  for  determining  the  contents  of 
a  given  log  by  this  rule  is, 

D2       L 

where   V  =  volume  in  standards ; 

Z)  =  diameter  inside  of  bark  in  inches  at  the  small  end  of  the  log  to  be 

measured ; 
L  =  length  in  feet  of  the  log  to  be  measured. 

Directions. 

A.  Data  Required. — Use  the  data  collected  in  Problem  6. 

B.  Method  of  Procedure. 

1.  Compute  the  volumes  of  all  vSections  except  stump  and  tip  in  19-inch 

standards. 

2.  Enter  the  values  in  a  blank  column  on  the  analysis  sheet,  label  properly 

and  total. 

PROBLEM  15.     (Field.)     The  Determination  of  the  Contents  of  Standing 
Trees  by  Short  Methods. 

Explanation. — It  is  often  necessary  to  determine  the  contents  of  standing  trees 
by  some  short  rule  of  thumb  when  no  volume  table  or  other  better  means  is 
available.  The  student  will  find  it  very  convenient  to  have  one  or  more  of 
these  short  rules  at  his  constant  command.  Each  of  these  methods  should 
be  tried  out  on  12  trees,  except  method  II  of  Illustration  1,  which  will  be 
used  in  connection  with  Problem  23. 

Illustration  1.— To  Compute  Contents  in  Board  Feet  of  Standing  Trees  by 
the  Spaulding  Rule. 


26  PRELIMINARY   CALCULATIONS 

Explanation. — The  Spaulding  Rule  is  well  adapted  for  Pacific  Coast  timber. 
The  original  Spaulding  Rule  was  based  u[)on  diagrams  but  the  following 
rule  of  thumb  gives  approximately  the  same  result. 

Vol  =  (/^-— 3D)—  plus  3  per  cent  to  G  per  cent  of  the  value  obtained  by 
this  formula. 

D  R  H  -I--D  R  H 

where   D  =  — '—^ — — - — '-    '- —  and  in  which  the  D.B.H.  is  the  diameter  breast 

high  inside  the  bark,  in  inches. 

L  =  length  from  top  of  stump  to  point  at  which  diameter  inside  bark  is 
equal  to  one-half  the  D.B.H.  inside  bark.  In  practice  it  makes 
little  difference  whether  this  length  be  estimated  with  the 
\  D.B.H.  point  taken  as  one-half  the  D.B.H.  outside  the  bark  or 
one  half  the  D.B.H.  inside  the  bark  as  long  as  both  measurements 
are  taken  either  inside  or  outside  the  bark. 

The  first  part  of  the  fo  nula,  namely  that  without  the  addition  of  the 
3  to  6  per  cent  will  give  thv.  volume  of  the  tree  up  to  the  \  D.B.H.  point. 
The  additional  3  to  6  per  cent  will  give  the  value  of  the  merchantable  portion 
of  the  tree  above  the  \  D.B.H.  point.  In  the  case  of  trees  with  very  tapering 
tips  above  the  \  D.B.H.  point,  the  lower  percentage,  namely  3  per  cent,  should 
be  used,  while  for  trees  without  excessive  taper  above  the  \  D.B.H.  point  a 
higher  percentage,  up  to  6  per  cent  should  be  used.  To  compute  the  volume 
by  this  formula  two  measurements  of  the  tree  are  necessary,  the  D.B.H. 
and  the  length  from  stump  to  \  D.B.H.,  which  will  be  obtained  as  outlined 
in  the  method  of  procedure. 

Directions. 

A.  Parties. — Men  will  be  organized  in  two-man  parties,  each  man  alternating 

as  cruiser  and  tallyman. 

B.  Equipment  Required  per  Party. 

1  pair  tree  calipers. 

1  hypsometer. 

1  dendrometer  (if  available). 

1  field  note  book  supplied  with  Form  3  A, 

C.  Method  of  Procedure. 

Method  1. — By  tallying  D.B.H.  and  merchantable  length  for  each  tree. 

1.  Caliper  D.B.H.  outside  bark  of  the  trees  whose  volumes  are  to  be 

computed. 

2.  By  estimate  determine  width  of  bark  at  breast  height,  and  check 

thickness  of  bark  occasionally  by  chipping  through  it. 


CONTENTS  OF  STANDING  TREES  BY  SHORT  METHODS      27 

3.  Estimate,  checking  the  estimate  occasionally  with  hypsometer,  the 

height  from  stump  up  to  5  D.B.H.  outside  bark. 

4.  Tally  these  three  measurements  on  Form  3  A,  using  one  vertical 

column  for  each  species.  On  the  left-hand  side  of  the  column, 
opposite  the  proper  D.B.H.  class,  enter  the  width  of  bark  and  on 
the  right-hand  side  the  height  up  to  |  D.B.H.  for  each  tree  cal- 
ipered. 

5.  From  these  field  measurements  compute  the  volume  inside  bark 

of  each  tree  from  the  formula . 
Method  H. — By  tallying  the  D.B.H.  of  each  tree  and  securing  heights 
from  a  height  curve. 

1.  Caliper  D.B.H.  outside  bark  of  the  trees  whose  volumes  are  to  be 

computed. 

Note. — When  the  D.B.H.  of  a  tree  falls  at  a  point  where  the  bole  is  swell- 
butted  the  measurement  should  be  reduced  so  as  to  give  the  tree  the  average 
amount  of  taper  which  in  the  judgment  of  the  cruiser  the  conditions  will 
warrant,  for  otherwise  the  formula  will  give  results  too  high. 

2.  Take  measurements  of  D.B.H.,  width  of  bark,  and  merchantable 

length  to  ^  D.B.H.  on  at  least  30  fallen  trees  of  various  sizes. 

3.  From  these  measurements  construct  a  height  curve  showing  mer- 

chantable heights  for  different  diameters  breast  high  outside  bark. 

4.  Using  an  average  width  of  bark  for  each  D.B.H.  and  with  heights 

obtained  from  the  height  curves,  compute  volumes  inside  bark 
with  the  Spaulding  Log  Rule,  for  trees  20,  30,  40,  50,  60,  70  inches 
D.B.H.  outside  bark. 

5.  Plot  the  volumes  of  the  sizes  thus  computed,  connect  with  a  curve, 

and  read  off  the  volumes  of  the  intermediate  diameters  breast 
high  outside  bark. 

6.  Tally  the  volumes  thus  obtained  in  tabular  form,  and  use  this  table 

for  computing  the  volumes  of  trees  calipered. 
Illustration  2. — To  Compute  the  Contents  of  Standing  Trees  in  Board  Feet 

by  the  Doyle  Rule. 
Explanation. — The  Doyle  Rule  is  simpler  than  the  one  described  above  but 

is  not  accurate  for  Pacific  Coast  timber,  since  it  will  give  high  results,  as  is 

the  case  when  this  rule  is  used  with  large-sized  logs  in  any  region.     The 

rule  follows : 


Volume  of  tree  =  (  — — -  )   XL. 


m 


D  =  middle  diameter  inside  bark  obtained  by  averaging  the  diameters  at  the 

top  and  base  of  the  merchantable  length  of  the  tree; 
L  =  merchantable  length. 

Directions. 

To  apply  the  Doyle  Rule  follow  Illustration  I,  Method  I,  described  above, 
except  that  the  middle  diameter  should  be  tallied  instead  of  D.B.H. 


28 


PRELIMINARY   CALCULATIONS 


Illustration  3. — To  Compute  Contents  of  Standing  Trees  in  Cubic  Feet  or 
Cords. 

Explanation. — The  object  of  this  illustration  is  to  demonstrate  a  method  of 
determining  the  volume  of  standing  trees  in  cubic  feet  or  in  cords.  The 
Schiffel  formula  (see  Problem  13,  Illustration  2)  may  be  used  for  computing 
the  volumes  in  cubic  feet  and  the  contents  in  cords  may  be  determined  by 
dividing  the  total  cubic  volume  by  90.  This  converting  factor  of  90>  is  based 
upon  the  supposition  that  a  cord  of  wood  contains  70  per  cent  solid  wood. 
This  of  course  will  vary  with  the  method  of  piling,  and  the  size  and  form  of 
the  pieces.  Should  the  trees  be  crooked  or  knotty,  and  the  wood  be  split  in 
small  pieces,  or  should  wood  be  wasted  in  the  stump  or  top  a  converting 
factor  between  80  and  90  should  be  used;  on  the  other  hand,  should  the 
timber  be  very  smooth,  straight  and  be  cut  in  very  large  pieces  a  factor 
between  90  and  100  should  be  used. 


Directions. 

A.  Parties. — Use  the  same  party  organization  as  for  Illustration  1. 

B.  Equipment  Required  Per  Party. — Use  the  same  equipment  as  for  Illus- 

tration 1,  except  that  Form  1  should  be  substituted  for  Form  3  A. 

C.  Method  of  Procedure. 

1.  Prepare  Form  1  with  the  following  column  headings  on  a  separate 
sheet  for  each  species : 


0. 


D.B.H. 


Total  Height 


D.M.H. 


Vol.  Cu.  Ft.      Vol.  Cords 


The  D.M.H.  column  will  be  used  for  tallying  the  diameter  at  the  mid- 
dle of  the  total  height.  The  D.M.H.  and  total  height  of  each  tree 
should  be  tallied  opposite  its  D.B.H. 

Caliper  the  D.B.H.  outside  the  bark  of  each  tree. 

Estimate,  checking  occasionally  with  a  hypsometer,  the  total  height 
of  each  tree. 

Estimate,  checking  with  a  dendrometer  if  available,  the  D.M.H.  out- 
side the  bark  of  each  tree. 

With  the  Schiffel  formula  work  up  the  cubic  volume  including  the  bark 
of  all  trees  and  total. 

Divide  the  total  volume  of  each  species  in  cubic  feet  by  90  to  redu(;e 
to  cords. 


D.  RrftTcnccs. — Numbers  51,  G4,  and  tif). 


SECTION  V— THE  CONSTRUCTION   OF  VOLUME   TABLES 

Explanation. — The  problems  in  this  section  have  been  chosen  with  reference 
to  illustrating  a  number  of  fundamental  problems  which  may  serve  as  a 
basis  for  all  volume  table  studies.  Each  problem  illustrates  some  one  or 
more  specific  features.  These  are  emphasized  in  each  instance  in  the  ital- 
icized portions  of  the  titles. 

The  relation  of  the  specific  features  to  related  problems  are  brought  out 
by  special  questions. 

Caution. — In  the  problems  of  this  section  the  student  should  use  special  care 
to  label  all  work  completely.  The  co-ordinate  axes  should  be  labeled  with 
the  unit  being  used,  as  ''Volume  in  cubic  feet";  and  each  completed  curve 
and  table  should  contain  all  the  information  necessary  to  give  it  scientific 
accuracy.  Substantial  reductions  in  grade  will  be  made  for  any  work  turned 
in  that  is  not  properly  and  completely  labeled. 

The  following  points  should  be  considered  in  the  title  of  a  completed 
volume  table,  though  not  all  need  be  included,  because  some  one  condition 
may  be  wholly  obvious  from  some  others  already  stated : 

1.  Kind  of  table. 

2.  Species. 

3.  Forest  type. 

4.  Locality. 

5.  Number  of  trees  upon  which  table  is  based. 

6.  Top  diameter-limit  used. 

7.  Date. 

PROBLEM    16.     (Office.)     The   Construction   of   a   Merchantable   Volume 
Table  in  Board  Feet  Based  on  D.B.H.  Only. 

Directions. 

A.  Method. — Averaging  the  values  first  and  then  plotting  the  averaged  points. 

B.  Data  Required. — The  student  should  determine  first  just  what  field 
measurements  are  necessary  for  the  construction  of  a  volume  table  of  this 
kind.  (See  Problem  G.)  Before  beginning  the  work  he  should  ask  the 
instructor  whether  his  conclusions  on  the  j^oint  arc  right.  Use  Data 
Series  I  or  the  data  collected  in  Problem  6.  In  case  the  latter  are  used 
the  field  work  of  the  entire  class  should  be  used  by  each  student. 

29 


30        THE  CONSTRUCTION  OF  VOLUME  TABLES 

C.  Method  of  Procedure. 

A.  Tabulation 
1 .  Divide  a  piece  of  blank  note  paper  into  tabular  form  with  the  following 
headings. 


One  Inch 

Tallied  Values 

Averaged  Values 

D.B.H. 

Classes 

Tallied 
D.B.H. 

Volumes 
B.M. 

No.  of 
Trees 

Average 
D.B.H. 

Average 
Volumes 

11"  Class 
10.6  to  11.5" 

12"  Class 
11.6"  to  12.5" 

The  horizontal  lines  should  be  spaced  far  enough  apart  to  allow  the 
data  for  all  trees  included  in  any  1-inch  diameter  class  to  be  listed 
between  them  in  a  vertical  column . 

Label  the  spaces  successively  with  the  diameter  classes  they  are  to 
represent. 

2.  Tally  in  a  vertical  column  in  the  space  allotted  to  the  D.B.H.  measure- 

ments the  actual  breast  high  diameters  to  the  nearest  0.1  of  an  inch, 
placing  each  in  the  space  allotted  to  its  class,  as  determined  by  the 
rule  that  each  class  shall  contain  all  trees  whose  diameters '  range 
from  .6  of  the  one  inch  to  .5  of  the  next  inch  higher,  inclusive. 

3.  In  the  second  column  enter  opposite  each  D.B.H.  tallied  the  calculated 

volume  of  the  tree  in  board  feet. 

4.  In  the  third  column  enter  the  number  of  trees  in  each  diameter  class. 

5.  When  all  the  trees  have  been  tallied,  add  the  actual  D.B.H.  measure- 

ments in  each  class, as  recorded  in  the  first  column,  and  divide  by  the 
total  number  of  trees  in  the  class  as  recorded  in  the  third  column  to 
obtain  the  average  D.B.H.,  and  record  it  in  the  fourth  column  oppo- 
site its  diameter  class. 

6.  In  a  similar  way  add  the  separate  volumes  in  each  class  as  recorded 

in  the  second  column,  and  divide  by  the  number  of  trees  in  the  class 
to  obtain  the  average  volume,  and  record  in  the  fifth  column . 
B.  Plotting. 

7.  On  a  sheet  of  cross-section  paper  lay  off  diameters  (D.B.H.)  and  vol- 

umes as  co-ordinates.  Determine  first  which  will  be  abscissa;  and 
which  ordinates  and  be  careful  to  select  values  for  each  commensurate 
with  the  limits  of  variation  in  the  data  and  the  size  of  the  cross- 
section  paper. 

8.  Plot  the  average  values  as  determined  and  recorded  in  the  tables,  and 

enter  beside  each  plotted  point  the  number  of  trees  it  represents. 


FULL  8TEM   CUBIC   FOOT  VOLUME  TABLE 


31 


9.  Connect  the  consecutive  average  points  by  fine  straight  hnes. 

10.  Draw  a  free-hand  curve,  giving  weight  to  the  various  points  according 

to  the  number  of  trees  represented,  and  smooth  off  the  curve  with  a 
si)hne  or  other  curve  rule. 

11.  Read  off  from  this  curve  the  volumes  for  whole  inches  as  indicated, 

and  tabulate  in  one  corner  of  the  sheet  of  cross-section  paper. 

12.  Label  the  exercise  and  indicate  the  species,  forest  type,  locality,  total 

number  of  trees  used,  and  date. 

D.  References.— lumbers  31,  32  and  36. 

PROBLEM    17.     (Office.)     The   Construction   of  a   Full  Stem   Cubic   Foot 
Volume  Table  Based  on  D.B.H.  and  Total  Heights. 

Method. — Averaging  the  values  first  and  then  plotting  the  averaged  values. 
For  this  problem  diameters  will  be  taken  in  2-inch  classes,  and  heights  in 
20-foot  classes.     (Ordinarily  heights  are  taken  in  10-  or  16-foot  classes.) 

Directions. 

A.  Data  Required. — Determine  first  just  what  field  measurements  are  neces- 

sary for  this  problem.     They  differ  slightly  from  those  of  Problem  16. 
Ask  the  instructor  if  you  are  right  before  proceeding. 

B.  Use  Data  Series  I,  or  the  data  collected  in  the  field  in  Problem  6. 

C.  Method  of  Procedure. 

I.  Tabulation. 
1 .  Prepare  a  blank  form  for  tabulation  like  the  following : 


20-FooT  Height  Classes 

Two-inch 
D.B.H. 

Classes 

80 

100 

120 

140                        Etc. 

1 

D.B.H. 

Vol- 
ume 

D.B.H. 

Vol- 
ume 

1 

D.B.H.      ""'- 
ume 

D.B.H.      ^'>'- 
ume 

D.B.H. 

Vol- 
ume 

12"  Class 
11.1" to  13.0" 

14"  Class 
13.1"  to  15.0" 

Each  diameter  class  will  be  imderstood  to  include  all  trees  from  .1 
over  the  whole  inch  of  one  diameter  to  the  whole  inch  of  the  second 
higher  diameter  inclusive;    i.e.,  the  12-inch  class  includes  all  trees 


32  THE  CONSTRITCTION   OF   VOLUME  TABLES 

from  111  inclics  to  !;>.()  iiiclics  iiu'liisivc;  and  all  lici^htclasses  from 
9  feet  below  to  the  even  10  feet  above  the  value  iiulicating  the 
class;  i.e.,  the  80-foot  height  class  includes  all  trees  from  71  feet  to 
90  feet  inclusive. 

2.  Record  the  D.B.H.  and  computed  volume  of  each  tree  in  the  space 

allotted  to  it  according  to  its  D.B.H.  and  total  height.  Tally 
D.B.H.  in  inches  and  tenths,  and  full  stem  volume  in  cubic  feet  and 
tenths. 

3.  When  all  the  trees  are  tallied,  determine  the  total  diameter  and  total 

volume  for  each  diameter-height  class  by  adding  the  recorded  values 
and  divide  each  by  the  total  number  of  trees  added  to  obtain  the 
average  diameter  and  average  volume  of  that  class. 

n.  Plotting 

A  new  feature  in  plotting  the  values  for  this  exercise  arises  which  has  not  been 
explained  heretofore.  (See  Problem  8.)  Instead  of  having  one  dependent  and 
one  independent  variable  we  now  have  two  independent  variables  namely, 
diameters  and  heights;  and  the  volumes  as  the  one  dependent  variable.  Hence 
three  distinct  values  must  be  considered.  Since  a  single  plotted  point  on  a  piece 
of  cross-section  paper  cannot  express  more  than  two  values  it  now  becomes 
necessary  to  draw  a  series  of  harmonized  curves  b}^  means  of  which  it  is  possible 
to  express  the  three  values.  This  is  done  by  first  plotting  separate  "volume-on- 
diameter"  curves  for  each  height  class.  From  the  resulting  series  of  curves  we 
obtain  the  volumes  according  to -the  different  diameters  irrespective  of  average 
heights.  With  the  average  volumes  read  from  this  series  of  curves  we  now  con- 
struct a  series  of  "  volume-on-height "  curves  for  the  different  diameter  classes, 
and  from  them  obtain  the  final  values  as  follows: 

a.  Averaging  the  Diameters. 

1.  On  a  piece  of  cross-section  paper  lay  off  diameters  as  abscissae  and 

volumes  as  ordinates.  Since  several  curves  must  be  drawn  on  a 
single  sheet  of  cross-section  paper  it  will  be  well,  in  order  to  avoid 
confusion,  to  use  a  scale  such  that  1  inch  on  the  paper  will  repre- 
sent at  least  2|  inches  in  D.B.H.  values.  It  will  also  aid  if  the 
different  points  of  each  height  class  are  connected  with  lines  in 
different  colored  inks  or  crayons. 

2.  Plot  a  curve  for  the  first  height  class  using  each  of  the  average 

values  and  average  heights  under  that  class;  i.e.,  plot  a  curve 
for  the  80-foot  height  class  using  the  D.B.H.  and  volumes  on  the 
tabulation  sheet  in  a  vertical  column  under  this  class.  Besides 
each  plotted  point  place  the  number  of  trees  represented.  Join 
the  points  by  fine  lines  and  draw  a  smooth  curve.  Label  this 
curve  with  the  height  class  it  represents. 

3.  In  a  similar  manner,  with  the  same  values  for  abscissae  and  ordi- 

nates, and  on  the  same  sheet  of  cross-section  paper,  plot  the 


FULL  STEM.  CUBIC   FOOT   VOLUME   TABLE 


33 


values  and  draw  smooth  curves  for  each  one  of  the  remaining 
height  classes.     Label  each.     If  any  of  these  height  classes  con- 
tain but  few  or  chiefly  abnormal  trees,  the  curve  for  this  class 
must  be  interpolated  between  the  next  higher  and  lower  classes. 
4,  From  each  height  curve  now  read  the  average  volume  for  the 
respective  average  diameters  in  2-inch  classes  by  taking  the 
reading  at  every  even  inch. 
.  Averaging  the  Heights. — Up  to  this  point  we  have  evened  off  the 
volumes  according  to  the  average  diameters,  irrespective  of  heights. 
Hence  it  will  now  be  necessary  to  determine  what  the  average 
volumes  will  be  according  to  the  average  heights. 
1.  On  a  piece  of  cross-section  paper  lay  off  heights  as  abscissa;  and 

volumes  as  ordinates. 
~  2.  Now  construct  a  set  of  curves  similar  to  those  constructed  under 
''rt,"  except  that  a  separate  curve  is  constructed  for  each  diameter 
class,  using  the  new  volumes  read  from  the  first  set  of  curves  on 
the  average  heights.  Use  for  the  heights  in  this  plotting  the 
value  indicating  the  cla'^s. 
3.  Read  off  the  values  for  every  even  20  feet  and  tabulate  in  the  final 
form  as  follows: 


D.H.B. 

Height  Classes 

Classes 

80 

100 

120 

140 

Etc. 

12 
14 

16 

Volume 
Volume 
Volume 

Volume 
Volume 
Volume 

Volume 
Volume 
Volume 

Volume 
Volume 
Volume 

Volume 
Volume 
Volume 

Label  every  curve  of  this  exercise  completely,  and  put  a  legend  on 
the  final  table  showing  the  type  of  volume  table  constructed,  the 
species,  the  number  of  trees  upon  which  the  table  is  based,  the 
unit  of  measure,  and  the  diameter  limit  used  in  computing  the 
volumes  of  the  trees. 


D.  /^e/cre^e.s.— Numbers  39,  41,  42,  43,  44  and  62. 

E.  Discussion. 

1.  Of  what  use  is  a  volume  table?     Can  it  be  applied  accurately  for 

securing  the  value  of  a  single  tree?     Why,  or  why  not? 

2.  In  what  respect  would  the  method  of  procedure,  outlined  above,  be 

varied  if  the  table  should  be  constructed  in  board  feet  instead  of 
cubic  feet? 


34        THE  CONSTRUCTION  OF  VOLUME  TABLES 

3.  What  is  the  difference  in  the  data  required  for  the  construction  of   a 

table  based  on  D.B.H.  only  and  one  based  on  D.B.H.  and  total 
heights? 

4.  Which  of  the  two  tables  would  be  the  more  accurate  and  why?    Which 

would  be  easier  to  use? 

5.  How  many  trees  would  ordinarily  be  considered  the  minimum  for  a 

good  D.B.H.  only  volume  table?  For  a  D.B.H.  and  total  height 
table? 

6.  Outline  stej)  by  step  and  in  detail  the  nu^thod  of  procedure  in  a  manner 

similar  to  that  used  in  Problem  17  for  making  a  table  based  on 
D.B.H.  and  number  of  16-foot  logs. 

7.  What  are  the  chief  details  in  which  the  construction  of  a  table  based 

on  D.B.H.  and  merchantable  lengths  differ  from  the  method  of 
procedure  outlined  in  Question  6? 

8.  Describe  briefly  how  a  cordwood  table  based  on  D.B.H.  would  be 

constructed. 

9.  Describe  briefly  how  a  tie  table  based  on  D.B.H.  would  be  constructed. 

PROBLEM   18.     (Office.)     The  Construction  of  a  Table  of  Stem  Form 
Factors  Based  on  D.B.H .  Only. 

Explanation:  The  object  of  this  problem  is  to  illustrate  the  method  of 
constructing  a  table  of  form  factors  and  to  show  the  difference  between  such 
a  table  and  a  volume  table. 

Directions: 

A.  Data  Required.     Use  the  data  collected  in  Problem  6. 

B.  Method  of  Procedure. 

1.  First  compute  the  full  stem  volumes  of  the  trees  in  cubic  feet  as 

explained  in  Problem  13,  Illustration  I. 

2.  Divide  the  computed  volume  of  each  tree  by  the  cubic  contents   of  a 

cylinder  whose  diameter  is  the  same  as  the  D.B.H.  of  the  tree,  and 
whose  height  is  equal  to  the  total  height  of  the  tree.  Call  the 
results  the  "form  factor  fractions."  For  determining  the  contents 
of  the  respective  cylinders  use  the  tables  of  Basal  Areas  in  the 
Appendix  and  multiply  by  the  heights. 

3.  From  this  point  on,  the  method  of  constructing  the  tajjie  will  be  the 

same,  step  by  step,  as  outlined  for  Problem  16,  except  that  the 
expression  "form  factor  fraction"  is  used  in  place  of  "volume  in 
board  feet"  throughout  the  exercise. 

Note. — For  rough  work  the  Schiffel  formula  may  be  used  for  securing  the 
form  factor  directly  without  the  necessity  of  first  finding  the  cubic  volume  and 
then  dividing  this  volume  by  the  volume  of  a  cylinder.  By  the  Schiffel  formula 
the  form  factor  of  a  tree  is  equal  to  0.16  +  0.GGXQ2  where  Q  is  the  form  quotient, 
which  is  the  D.M.H.  divided  by  the  D.B.H.,  where  the  D.M.H.  equals  the  diam- 
eter at  the  middle  height  of  the  tree. 


VOLUME  TABLE  IN  BOARD  FEET  BASED  ON  D.B.H. 


35 


C.  Discussion. 

1.  What  is  the  difference  between  a  table  of  form  factors  and  a  volume 

table? 

2.  What  is  the  difference  in  their  uses? 

3.  Which  is  the  more  practical  for  ordinary  timber  estimating? 

PROBLEM  19.  (Field.)  The  Construction  of  a  Merchantable  Volume 
Table  in  Board  Feet  Based  on  D.B.H.  and  Number  of  IQ-Foot  Logs  by 
THE  Frustum  Form  Factor  Method. 

Explanation. — A  method  of  constructing  volume  tables  based  on  D.B.H. 
and  log  lengths  which  much  lessens  the  office  work  involved  and  which  will 
give  a  better  table  with  a  lesser  number  of  trees  has  been  devised  by  Mr. 
Donald  Bruce  and  is  described  by  him  in  the  Forestry  Quarterly,  Volume  X, 
Number  2  and  in  the  Proceedings  of  the  Society  of  American  Foresters, 
Volume  VIII,  Number  3.  This  method  has  not  gained  universal  use  and 
its  accuracy  compared  with  the  usual  method  of  constructing  volume  tables 
has  not  been  entirely  established.  Several  tests  have,  however,  shown  that 
excellent  results  can  be  obtained  with  the  method.  The  following  problem 
will  demonstrate  this  method  of  constructing  a  volume  table. 

Directions: 

A.  Data  Required. — About  25  trees  will  be  required  for  Method  I    and  100 

or  more  for  Method  II.  Use  data  collected  in  Problem  6,  or  trees  of 
different  sizes  w^hich  show  the  volumes  of  boles  in  board  feet  measured 
in  16-foot  lengths  to  an  8-inch  diameter  in  the  tops  selected  at  random 
from  Data  Series  I. 

B.  Method  of  Procedure. 

Method  I.  To  construct  a  volume  table  with  a  small  number  of  trees. 
1.  Tabulate  the  sizes  of  the  trees  to  be  used  in  this  problem  according  to 
the  following  form : 


D.B.H. 
Inches 


No.  16-ft.         Volume 

Logs  B.M. 

to  8"  Top   j   to  8"  Top 
Diameter    '    Diameter 


Frustum 
Form 
Factor 


Compute  the  frustum  form  factor  for  each  tree  by  dividing  the  volume 
of  the  tree  by  the  volume  of  the  corresponding  frustum  of  a  cone  as 
secured  from  the  table  of  frustums  of  cones  in  the  Appendi.x  (Table 
IV).  Interpolate  in  this  table  the  volumes  for  diameters  breast 
high  to  0.1  inch  and  lengths  to  the  nearest  ^  of  a  16-foot  log. 


36  THE  CONSTRUCTION   OF  VOLUME   TABLES 

3.  Find  the  averago  frustum  form  factor  by  obtaining  the  sum  of  the 

individual  form  factors  of  all  trees  and  dividing  by  the  number  of 
trees. 

4.  Obtain  the  volume  taV)le  by  multiplying  each  volume    in  the  frustum 

table  in  the  Appendix  by  the  average  frustum  form  factor. 

Method  IL  To  construct  a  volume  table  with  a  considerable  number  of 
trees. 

1.  Compute  the  frustum  form  factor  as  in  Method  L 

2.  Devise  a  convenient  form  of  tabulation   and  group  the  trees  into 

5-inch  diameter  classes.     Secure  for  each  class  the  average  frustum 
form  factor. 

3.  Round  off  the  values  of  these  average  frustum  form  factors  by  means 

of  a  curve. 

4.  Obtain  the  final  volume  table  by  multiplying  each  value  in  the  frustum 

table  in  the  Appendix  by  the  average  frustum  form  factor  for  the 
diameter  class  in  which  the  value  is  included. 

Note. — Should  the  table  in  the  Appendix  giving  the  volumes  of  frustums 
of  cones  not  contain  a  sufficient  range  of  values  it  may  be  extended  by  the 
method  illustrated  in  the  following  two  examples: 

Example  1.  To  find  the  volume  of  the  frustum  of  a  cone  with  8-inch  top, 
10  inches  D.B.H.  and  H  logs  in  length. 
Tree:    10  inches  D.B.H.  with  8-inch  top  and  1  log  in  length  yields  1  8-inch 
log  containing  32  feet  B.M. 

Tree:    10  inches  D.B.H.  with  8-inch  top  and  2  logs  in  length  yields 
1     8-inch  log  containing  32  feet  B.M. 
1     9-inch  log  containing  42  feet  B.M. 


Total  volume.  .  .  .■ 74  feet  B.M. 

By  Interpolation 

Tree:   10  inches  D.B.H.  8-inch  top  1|  logs  in  length  yields  32  +  K74-32)  = 
43  feet  B.M. 

Example  2.  To  find  the  volume  of  the  frustum  of  a  cone  with  8-inch  top, 
16  inches  D.B.H.  and  4  logs  in  length. 

Total  taper  =  8  inches.     Taper  per  log  =  2  inches. 

Tree  yields  1  8-inch  log  containing    32  feet  B.M. 

1  10-inch  log  containing    54  feet  B.M. 

1  12-inch  log  containing    79  feet  B.M. 

1  14-inch  log  containing  114  feet  B.M. 

Total  volume 279  feet  B.M. 


THE  CONSTRUCTION  OF  A  TAPER  TABLE        37 

C.  References. — Numbers  33,  34  and  40. 

D.  Discussion. 

1.  What  is  gained  over  Method  I  by  using  IVIethod  II? 

2.  Compare  the  frustum  form  factor  method  and  the  regular  method  of 

constructing  volume  tables  as  to  time  required  and  as  to  accuracy. 

3.  How  might  the  table  bo  constructed  by  averaging  according  to  the 

number  of  16-foot  logs  as  well  as  according  to  D.B.H.  as  explained 
in  Method  H? 

PROBLEM  20.     (Office.)     The  Construction  of  a  Taper  Table. 

Expl.\nation:  Taper  Tables  show  for  each  D.B.H.  the  top  diameter  inside 
the  bark  of  the  respective  16-foot  logs  (the  usual  length  employed).  Such 
tables  can  be  used  in  place  of  volume  tables  in  cruising  where  the  trees  are 
tallied  according  to  the  D.B.H.  and  number  of  16-foot  logs.  This  method 
has  an  advantage  over  volume  tables  in  that  an  estimate  can  be  worked  up 
according  to  any  log  rule  or  any  one  of  the  units  of  log  measure.  It  presents 
the  disadvantage  of  requiring  more  subsequent  calculations  for  securing  the 
volume  of  an  estimate  than  does  the  use  of  volume  tables. 

Directions: 

A.  Data  Required. — Use  data  collected  in  Problem  6. 

B.  Method  of  Procedure.     (Prerequisite  study — Reference  Number  38.) 

1.  On  a  separate  sheet  of  cross-section  paper  for  each  20-foot  total  height 

class,  lay  off  heights  above  the  ground  as  abscissae  and  diameters 
inside  of  bark  as  ordinates. 

2.  Plot  all  trees  in  2-inch  D.B.H.  classes. 

3.  For  each  D.B.H.  class  plot  points  representing  the  D.I.B.  at  the  top 

end  of  each  16-foot  log  section.  If  possible,  plot  all  curves  on  one 
sheet  using  a  different  symbol  (.,  x,  o,  O,)  for  each  diameter  class  in 
order  to  keep  the  various  classes  separate. 

4.  Average  points  for  each  16-foot  section  of  each  D.B.H.  class,  and 

construct  regular  curves  for  each  D.B.H.  class. 

5.  Assume  an  arbitrary  stump  height  (e.g.,  3  feet),  and  read  off  the  D.I.B. 

values  for  each  16-foot  section. 

6.  For  the  same  20-foot  total  height   classes  and   u^ith  the  same  ordi- 

nates but  using  D.B.H.  for  abscissae,  replot  and  average  the  data 
in  separate  16-foot  classes  above  the  stump. 

7.  From  the  averaged  data  found  in  6,  for  each  2-inch  D.B.H.  class  plot 

a  series  of  16-foot  curves  above  the  stump,  using  the  same  ordi- 
nates and  the  total  heights  of  trees  as  abscissae. 

8.  With  the  averaged  data  from  7   now   plot  a   fourth   set  of  curves 

exactly  as  was  done  in  1  and  then,  with  the  data  thus  obtained, 
plot  a  fifth  set  of  curves  as  was  done  in  6.  Retain  the  data  thus 
obtained  in  graphic  form  or  read  off  a  set  of  tables. 


SECTION  VI— SCALING 

PROBLEM  21.     (Field.)     Scaling  Logs. 

Explanation:  The  method  of  scahng  sound  logs  free  from  any  defect  or 
malformation  is  very  simple.  All  it  requires  is  that  the  diameter  inside  the 
bark  at  the  small  end  of  the  log  and  the  length  of  the  log  be  measured  and 
with  these  two  measurements  the  corresponding  volume  in  board  feet  may  be 
found  on  a  scale  stick  or  in  a  table  giving  contents  of  logs  according  to  the 
log  rule  used.  Should  the  lengths  of  logs  to  be  scaled  be  limited  to  a  certain 
maximum  length,  logs  longer  than  this  length  should  be  scaled  in  two  sections 
of  as  nearly  equal  even-foot  lengths  as  possible,  the  shorter  length  to  be 
taken  at  the  small  end  of  the  log.  The  diameter  of  the  section  nearest  the 
large  end  of  the  log  should  be  increased  over  the  diameter  at  the  small  end 
by  an  amount  corresponding  to  the  taper,  estimated  for  each  log.  The  sum 
of  the  volumes  of  the  two  sections  will  give  the  volume  of  the  log. 

However,  no  method  of  scaling  is  accurate  unless  the  sound  volume  is 
discounted  to  allow  for  defects  which  may  occur  in  the  log.  The  following 
formulae  and  tables  together  with  an  explanation  of  the  method  of  their  use 
will  demonstrate  typical  methods  of  allowing  for  defect  in  scaling. 

FormuloB  for  Scaling  Defect 


Pitch  Seams 

OC^C^^i^E^  T  =  DDXL 

V    12    7  5        15 

W=  width  of  seam  across  end  of  log,  inches; 
A  =  waste  thickness,  inches; 
12  =  dividing  factor,  to  reduce  to  B.M. 
DD  =  defect  deduction  per  lineal  foot  in  feet  B.M, 
L  =  length  of  defect,  feet; 

1^  =  reducing  factor,  to  allow  20  per  cent  for  sawkerf; 
T  =  total  number  feet  B.M.  defect  caused  by  seam. 


SCALING  LOGS  39 

Pitch  Rings 


DD=(''-^Y  =  0.2iDXA)  T  =  DDXL. 

\     12     /  5 

D  =  diameter  of  ring,  inches; 
7r  =  3.14. 

Remaining  factors  same  as  for  pitch  seams. 


Rot 


4     W^ 
DD=  {  —  ]-  =  —,  T  =  DDXL. 


\12/- 


TT^=side  of  a  square  which  can  be  circumscribed  around  the  defect, 
inches; 


Shingle  Bolts 


144 

^  =  area  of  end  of  bolt,  square  inches; 

L  =  length  of  bolt,  inches ; 
144  =  dividing  factor  to  reduce  to  B.M.; 
.70  =  per  cent  of  utilization; 

y  =  total  number  feet  B.M.  in  bolt. 


Explanation  of  Scaling  Formulae 

There  are  various  systems  of  m.aking  allowance  for  the  defects  which 
occur  in  logs  but  the  simplest  and  most  logical  is  to  consider  the  amount  of 
the  defect  as  equivalent  to  the  piece  of  lumber  which  would  be  lost  in  sawing 
it  out  in  the  saw  mill.  As  tl^  Scribner  rule  makes  an  allowance  for  sawkerf 
of  J  inch  for  each  1-inch  board  or  a  deduction  of  20  per  cent  of  the  volume 
of  the  log  this  deduction  should  also  be  taken  into  account  in  making  the 
defect  allowance. 

In  the  formulae  the  defect  deduction  is  first  found  per  lineal  foot  and 
then  multiplied  by  the  length  of  the  defect  as  this  is  the  easiest  procedure 
for  the  scaler  to  follow  in  practice  as  will  be  e.xplained  below  for  each  type  of 
defect. 

Pitch  Seam. — To  determine  the  amount  of  defect  in  a  log  with  a  pitch 
seam  or  seams  the  scaler  should  determine  if  they  show  on  both  ends  of  the 
log  and  whether  they  are  straight  or  twisted,  for  the  greater  the  twist  the 


40  SCALING  LOGS 

greater  will  be  the  amount  of  waste.  Sometimes  a  seam  at  one  end  of  the 
log  will  be  at  right  angles  to  its  position  on  the  opposite  end.  If  the  seam 
shows  on  one  end  only,  the  scaler  should  estimate  the  length  it  extends  into 
the  log  .and  take  as  the  width  of  the  seam  its  width  as  it  shows.  If  the  seam 
shows  at  both  ends  of  the  log  the  width  of  the  seam  should  be  taken  at  Avhich- 
ever  end  it  is  the  greatest. 

Measure  the  width  of  the  seam  across  the  end  of  the  log  and  the  inches 
of  waste  that  will  result  from  sawing  out  the  seam.  Multiply  the  width  of 
the  seam  by  the  thickness  of  the  waste,  divide  by  12,  and  multiply  the  result 
by  ^,  which  will  give  the  number  of  feet  B.M.  defect  per  lineal  foot.  Multiply 
this  by  the  length  of  the  defect  and  the  result  will  be  the  total  number  of  feet 
B.M.  defect  caused  by  the  seam.* 

Pitch  Ring. — To  determine  the  amount  of  defect  in  a  log  with  a  full 
pitch  ring  the  scaler  should  first  determine  if  the  ring  shows  on  both  ends  of 
the  log.  If  it  does  not  show  on  both  ends  he  should  estimate  the  number 
of  feet  it  extends  in  the  log,  and  then  measure  the  diameter  of  the  ring.  If 
it  shows  on  both  ends  he  should  average  the  diameters  of  the  rings  on  both 
ends.  Care  should  be  used  in  getting  this  average  diameter  in  swell  butted 
logs  so  as  to  get  a  fair  average,  for  the  ring  generally  tapers  with  the  swell  and 
if  the  swell  is  very  great  the  measured  diameter  will  be  too  large. 

Multiply  the  diameter  of  the  ring  thus  obtained  by  3.14  to  obtain  the 
circumference  and  then  measure  or  estimate  the  number  of  inches  of  waste 
necessary  to  saw  out  the  ring — the  inches  of  waste  depending  upon  the  irregu- 
larity of  the  ring.  When  two  rings  occur  close  together  a  large  factor  of 
waste  must  be  taken  as  no  lumber  can  be  cut  between  the  rings. 

Multiply  the  circumference  by  the  thickness  of  waste,  divide  by  12  and 
multiply  the  result  by  ^.  This  will  give  the  number  of  feet  B.M.  defect 
per  lineal  foot.  Multiply  this  result  by  the  length  of  defect  and  the  result 
will  be  the  total  number  of  feet  B.M.  defect  caused  by  the  pitch  ring. 

Rot. — To  determine  the  amount  of  defect  in  a  log  with  center  or  stump  rot, 
the  scaler  should  first  determine  if  it  shows  on  both  ends  of  the  log.  If  it 
does  not  show  on  both  ends  he  should  estimate  the  number  of  feet  it  extends 
into  the  log  and  then  measure  its  diameter.  If  it  shows  on  both  ends  he  should 
average  the  diameters  if  the  rot  is  uniform  throughout  the  length  of  the  log. 
Care  must  be  taken  with  swell  butted  logg  to  get  an  average  diameter  as  the 
rot  usually  tapers  very  rapidly  in  such  logs.  When  such  logs  have  rot  of 
large  diameter  at  one  end  and  rot  of  small  diameter  at  the  other  end  it  is 
well  to  divide  the  length  of  the  rot  into  sections  and  give  each  section  a 
diameter  estimated  according  to  the  taper  of  the  rot.  Each  section  would 
then  be  treated  as  a  unit  by  itself  and  the  total  of  the  defect  for  each  would 

*  Since  in  scaling  with  most  log  rules  all  material  outside  the  cylinder  represented  by  the 
top  end  diameter  is  considered  as  lost  in  slabbing,  a  defect  which  shows  at  the  butt  end  of  a 
log  should  never  be  taken  as  larger  than  the  top  diameter  of  the  log  unless  the  log  is  scaled 
in  two  sections,  as  explained  in  Problem  12.  In  this  case  the  defect  at  the  butt  of  the  log 
should  not  be  taken  as  larger  than  the  top  diameter  of  the  butt  section. 


SCALING  41 

give  the  total  defect  for  the  lojj;.  It  will  be  noted  that  the  ro(.  formula  is 
similar  to  the  pitch  seam  formula  except  that  the  width  of  the  defect  is 
taken  as  equal  to  the  diameter  of  the  rot. 

Slab. — Western  red  cedar  logs  in  the  course  of  handling  very  often  si)lit 
up  into  slabs  which  can  not  be  acciu*ately  scaled  as  logs.  The  method  used 
on  the  Pacific  Coast  in  this  case  is  to  estimate  the  volume  of  the  slab  in 
shingle  bolts  and  reduce  this  volume  to  feet  B.M.  by  the  formula  given 
above.  A  ''shingle  bolt "  in  the  formula  is  a  piece  52  inches  in  length  with 
roughly,  equilateral  triangular  ends,  the  sides  of  this  triangle  being  12,  14,  16, 
or  18  inches  in  length.  To  determine  the  number  of  feet  B.M.  in  a  shingle 
bolt,  first  measure  the  end  and  compute  the  area  of  it  in  square  inches,  then 
multiply  by  the  inches  m  length  and  divide  by  144.  Multiply  this  result  by 
.70  and  the  result  will  be  the  number  of  feet  B.M.  in  the  bolt. 

Example:  How  many  feet  B.M.  in  a  bolt  52  inches  in  length  which  has 
a  triangular  cross  section  18  inches  on  a  side? 

Area  of  triangle  (18  by  18  by  18)  X  52  ^       ^  ,  , 

X./0  =  35  feet  B.M. 

144 

Miscellaneous  Defects. — The  formula?  just  given  for  seams,  rings,  and  rot 
can  be  applied  to  nearly  all  other  interior  defects.  There  are,  however, 
several  other  types  of  defects  to  which  they  do  not  exactly  apply,  such  as 
crook,  cat  face,  sap  rot,  worms,  broken  ends,  etc.  Allowance  for  crook  can 
be  made  by  a  lump  percentage  of  the  total  contents  of  the  log  or  by  deducting 
the  equivalent  of  the  piece  of  lumber  which  it  is  visualized  would  be  lost. 
No  allowance  is  made  for  cat  face  or  similar  side  defects  unless  they  extend 
inside  the  cylinder  represented  by  the  top  diameter  of  the  log,  in  which  case 
the  equivalent  of  the  piece  of  lumber  lost  should  be  computed  and  deducted. 
Allowance  for  sap  rot  will  be  made  by  scaling  the  log  with  a  diameter  inside 
the  exterior  decay.  Worms  and  broken  ends  can  be  allowed  for  by  reducing 
the  length  of  the  log  sufficiently  to  eliminate  the  defect. 

Method  of  Using  Scaling  Tables 

In  order  to  simplify  the  application  of  the  method  to  actual  scaling,  by 
means  of  the  scaling  formulae,  the  tables  on  page  42  have  been  computed 
to  show  the  defect  per  lineal  foot  for  the  most  common  sizes  encountered  in 
scaling.  A  copy  of  these  tables  should  be  carried  by  the  scaler  for  reference 
at  all  times. 

Included  with  the  scaling  tables  is  a  legend  for  use  in  indicating  on  the 
scaling  sheet  (Form  5)  the  kind  of  defect  found  in  each  log.  This  legend  may 
be  used  as  follows: 

If  a  log  has  a  pitch  ring,  use  the  letters  P.  R.  as  show^n  in  legend  instead 
of  writing  the  words  in  full. 

If  a  log  has  a  pitch  seam  and  ground  rot,  use  the  letters  P.  S.  and  G.  R. 

If  a  cedar  slab  is  scaled,  place  the  letters  SI  in  the  defect  column. 


42 


SCALING 


TABLES   FOR   SCALING    DEFECT 


Legend  for  Defect 


P.R. 
PS. 

S. 
SI. 
Sp. 
Sh. 

c. 

Cr. 

Ch. 

Ck. 

R. 

G.R. 

W. 

B. 

O.  L. 

Pk. 

Y. 


Pitch  ring 

Pitch  seam 

Shake 

Slab 

Split 

Shatter 

Conk 

Crook 

Check 

Chunk 

Rot  in  cedar 

Ground  or  stump  rot 

Worms 

Broken  end 

Overlength 

Punk  or  sap  rot 

Crotch 


Shingle  Bolts 


No. 

of 

Bolts 


Size 


18X18  16X16  14X14  12X12 


Bolts  per  Cord 


20     25     33     44 


Board  Feet 


35 

70 

105 

140 

175 

i  210 

i  245 

280 

315 

350 


28 
56 
84 
112 
140 
168 
196 
224 
252 
280 


21 

42 

63 

84 

105 

126 

147 

168 

189 

210 


16 

32 

48 

64 

80 

96 

112 

128 

144 

160 


Length 


4'  4' 


13' 

17' 

21' 

26' 

30' 

i  34' 

I  39' 

I  43' 


Pitch  Rings 


Pitch  Seam 


Rot 


Diameter 

or 

Width 


10 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
,35 
36 


Waste,  Thickness  Inches 


4    5    2    3    4 


Defect  per  Lineal  Foot 


4 

5 

6 

1 

2 

4 

6 

7 

1 

2 

5 

6 

8 

2 

2 

5 

7 

9 

2 

2 

6 

8 

10 

2 

3 

7 

9 

11 

1 

2 

3 

7 

10 

12 

2 

2 

3 

8 

10 

13 

2 

3 

3 

8 

11 

14 

2 

3 

4 

9 

12 

15 

2 

3 

4 

10 

13 

16 

2 

3 

4 

10 

14 

17 

2 

3 

5 

11 

14 

18 

2 

4 

5 

11 

15 

19 

2 

4 

5 

12 

16 

20 

3 

4 

5 

13 

17 

21 

3 

4 

6 

13, 

18 

22 

3 

4 

6 

14 

18 

23 

3 

5 

6 

14 

19 

24 

3 

5 

6 

15 

20 

25 

3 

5 

7 

16 

21 

26 

3 

5 

7 

16 

22 

27 

4 

5 

7 

17 

22 

28 

4 

6 

8 

17 

23 

29 

4 

6 

8 

18 

24 

30 

4 

6 

8 

19 

25 

31 

4 

6 

8 

1« 

26 

32 

4 

6 

9 

20 

26 

33 

4 

7 

9 

20 

27 

34 

4 

7 

9 

21 

28 

35 

5 

7 

9 

22 

29 

36 

5 

7 

10 

SCALING  LOGS  43 

/ 

Pif.ch  Ring,  Pitch  Seam  and  Rot  Tables. — These  tables  have  been  com- 
puted by  use  of  the  defect  formulae  explained  in  the  first  part  of  this  problem. 
In  the  pitch  ring  table  the  first  column  gives  the  diameter  of  the  ring,  the 
figures  below  "Waste  Thickness"  give  the  inches  waste  necessary  to  saw  out 
the  ring  and  the  figures  under  columns  3,  4,  5  show  the  number  of  feet  B.M. 
of  defect  per  lineal  foot.  The  pitch  seam  table  similarly  shows  the  defect 
for  different  waste  thicknesses  and  widths.  The  rot  table  shows  the 
defect  for  different  average  diameters.  In  each  case  the  defect  per  lineal 
foot  should  be  multiphed  by  the  total  length  of  the  defect  and  the  result 
subtracted  from  the  full  scale. 

Example:  If  a  log  has  a  pitch  ring  20  inches  in  diameter  and  a  waste 
thickness  of  4  inches,  the  defect  in  board  feet  per  lineal  foot  wiU  be  found  in 
the  column  headed  "4"  under  "Pitch  Rings"  opposite  20  in  the  "Diam." 
column,  which  in  this  case  is  16  board  feet.  Multiply  this  defect  per  lineal 
foot  by  the  distance  the  pitch  ring  extends  into  log  and  the  result  will  be  the 
total  number  of  feet  B.M.  defect  caused  by  the  ring. 

Example:  If  a  log  has  a  pitch  seam  16  inches  in  width  across  the  end  of 
the  log  and  a  waste  thickness  of  2  inches  the  defect  in  board  feet  per  lineal 
foot  will  be  indicated  in  the  column  headed  "2"  under  "Pitch  Seam"  oppo- 
site 16  in  the  "Diam."  column,  which  in  this  case  is  2  board  feet.  Multiply 
this  defect  per  lineal  foot  by  the  distance  the  seam  extends  into  the  log,  and 
the  result  will  be  the  total  number  of  feet  B.M.  defect  caused  by  the  seam. 

Example:  If  a  log  has  a  uniform  rot  16  inches  in  diameter,  the  defect  in 
board  feet  per  lineal  foot  will  be  indicated  in  the  column  headed  "Rot" 
opposite  16  in  the  "Diam."  column,  which  in  this  case  is  17  board  feet. 
Multiply  this  defect  per  lineal  foot  by  the  distance  the  rot  extends  into  the 
log  and  the  result  will  be  the  total  number  of  feet  B.M.  defect  caused  by  the 
rot. 

Shingle  Bolt  Table. — By  means  of  the  formula  for  securing  the  contents 
of  shingle  bolts  the  table  above  has  been  computed  to  show  the  contents  in 
board  feet  of  bolts  52  inches  long  with  triangular  ends  18X18X18, 
16X16X16,  14X14X14,  and  12X12X12  inches.  Under  each  column 
heading  giving  the  size  of  the  bolt  is  showm  a  figure  representing  the  number 
of  bolts  of  that  size  contained  in  a  cord  and  in  the  table  below  is  shown  the 
board  foot  contents  of  any  number  of  bolts  from  one  to  ten  inclusive.  In 
the  last  column  under  "length"  is  shown  the  length  in  feet  corresponding 
to  the  number  of  bolts  indicated  in  the  first  column. 

In  using  this  table  for  scaling  slabs  the  scaler  should  first  ascertain  what 
size  bolts  the  cross  section  of  the  piece  is  equivalent  to  and  then  estimate 
the  number  of  that  size  bolts  contained  in  the  piece.  The  number  of  board 
feet  in  the  piece  may  then  be  secured  by  referring  to  the  shingle  bolt  table. 

Should  the  cross  section  of  the  slab  be  larger  than  an  18X18X18  bolt  it 
may  be  divided  into  bolts  of  two  sizes  {i.e.,  18X18X18  and  12X12X12,  etc.), 
and  the  number  of  such  bolts  and  their  equivalent  board-foot  contents 
secured. 


44  SCALING 

Example:  A  slab  triangular  on  the  ends  measuring  18  inches  on  the  side 
and  40  feet  in  length  contains  nine  bolts.  The  scaler  looks  in  column  "No. 
of  Bolts"  and  finds  9;  then,  in  column  "18X18"  opposite  "9,"  in  the  first 
column,  he  finds  that  the  slab  contains  315  board  feet.  If  the  piece  con- 
tained 9  bolts  14X14  and  9  bolts  16X16,  the  table  indicates  that  9  bolts 
14X14  contain  189  board  feet,  and  9  bolts  16X16  contain  252  board  feet, 
and  the  sum  of  these  two  gives  the  total  number  of  441  board  feet  in  the  slab. 

Directions: 

A.  Parlies. — Each  man  will  work  by  himself  in  this  problem. 

B.  Equipment  Required. 

1  scale  stick; 

1  blue  lumber  crayon; 

1  field  note  book  supplied  with  Form  5; 

1  copy  of  table  for  scaling  defect. 

C.  Method  of  Procedure. 

1 .  In  an  area  in  which  logs  are  available  select  a  specified  number  of  logs 

for  scaling. 

2.  Number  the  top  end  of  each  log  consecutively  and  place  this  number 

in  the  proper  column  in  the  form  in  order  that  the  instructor  may 
check  the  scaled  contents. 

3.  Scale  the  sound  contents  of  each  log  in  accordance  with  directions 

given  in  Problem  12.  Estimate  or  actually  measure  the  taper  of 
a  log  when  it  is  divided  into  two  or  more  sections  in  applying  the 
maximum  scaling  length. 

4.  Inspect  the  log  carefully  to  ascertain  whether  it  has  any  defects  and 

if  it  has  make  the  deductions  by  means  of  the  scaling  table  in  accord- 
ance with  the  principles  outlined  above. 

5.  Tally  the  net  scale  in  the  proper  column.     In  the  "Defect   Column" 

show  the  defect  by  symbol  and  amount.  If  the  scaling  is  done  by  the 
Scribner  Dec.  C.  Rule,  both  the  defect  and  the  net  scale  should  be 
tallied  to  the  nearest  ten  feet  B.M.  and  the  zero  to  show  the  full 
scale  added  only  to  the  total  net  scale  at  the  bottom  of  the  page. 

D.  i^e/erences.— Numbers  45,  46,  47,  48,  53  and  54. 


SECTION  VII— DETERxMINATION  OF  THE     CONTENTS  OF  STANDS 

Explanation:  This  section  has  been  outhned  especially  with  reference  to 
Pacific  Coast  timber.  Very  shght  modifications  to  suit  the  needs  of  the 
different  sections  of  the  country  will,  however,  make  it  available  for  use 
anywhere.  The  blank  pages  at  the  end  of  the  problems  may  be  used  for 
noting  such  modifications.  The  work  has  been  arranged  to  illustrate  several 
methods  of  cruising,  so  as  to  allow  the  student  to  compare  them,  and  to  give 
him  practice  in  estimating  the  total  volumes  of  trees  and  stands  by  ocular 
estimate. 

PROBLEM  22.     (Field.)     Obtaining   the   Contents  of  a  Small  Tract  of 
Timber  by  Different  Methods. 

Directions: 

A.  Parties. — Men  will  be  organized  in  two-man  crews,  each  man  alternating 

as  tallyman  and  as  cruiser. 

B.  Instruments. 

1  pair  tree  cahpers. 

1  compass. 

1  hypsometer. 

1  field  notebook,  supplied  with  Forms  1,  3  A,  B  and  4  A,  B. 

C.  Method  of  Procedure. 

1.  Select  a  representative  area  in  the  stand,  and  with  the  aid  of  the 

compass  and  paced  distances  run  out  a  square  acre  (208.7  feet  on  a 
side) . 

2.  Secure  the  volume  of  the  acre  tract  by  the  following  five  methods: 

(a)  Ocular  estimate. 

ih)   Commercial  cruising  method. 

{c)   D.B.H.  volume  table  method. 

{(I)  Diameter-height  volume  tabic  method. 

{c)   Spaulding  rule  method. 

These  methods  should  be  carried  out  in  the  following  way:    Each  of 

these  methods,  except  (c)  and  {d)  which  may  be  combined  in  the 

field,  should  be  worked  out  separately  in  the  order  given,  and  the 

volume  computed  on  the  ground  before  proceeding  with  the  next 

45 


46  DETERMINATION  OF  THE  CONTENTS  OF  STANDS 

method,  in  order  best  to  compare  them.  Make  no  deduction  for 
defect  or  breakage  and  include  all  standing  live  or  dead  trees  above 
12  inches  D.B.H.  since  the  object  of  the  exercise  is  to  compare  total 
volumes. 

(a)  Ocular  estimate. 

Before  measuring  or  counting  any  of  the  trees  make  an 
estimate  of  the  total  volume  of  the  tract.  The  succeeding 
methods  will  show  the  accuracy  of  your  estimate.  Use 
Form  1. 

(6)  Commercial  cruising  method. 

Count  all  the  trees  on  the  tract,  and  estimate  the  volume 
of  the  average  tree.  Multiply  this  volume  by  the  number  of 
trees  to  secure  the  total  volume  of  the  stand.  Check  the 
method  by  actual  measurement  of  what  is  judged  to  be  an 
average  tree,  calipering  its  D.B.H.,  measuring  the  height 
with  the  hypsometer,  and  computing  the  volume  by  the 
Spaulding  Rule  of  Thumb  (See  Problem  15,  Illustration  1, 
Method  I).  Use  Form  1  for  recording  the  measurements 
and  estimate. 

(c)  D.B.H.  volume  table  method. 

Caliper  the  diameter  breast  height  outside  the  bark  of  all 
trees  on  the  tract.  Compute  the  volume  of  the  tract  by  use 
of  the  volume  table  constructed  in  Problem  16,  or  any  other 
volume  table  based  on  diameters  breast  high  only,  which 
would  be  applicable  to  the  conditions.  Use  Form  3  A  for 
recording  the  measurements  and  estimate. 

(d)  Diameter-height  volume  table. 

Cahper  the  diameters  breast  high  outside  the  bark,  and 
estimate  the  total  heights  of  all  trees  on  the  tract.  As  a 
check  measure  with  a  hypsometer  the  heights  of  the  first  trees 
taken.  Compute  the  volume  of  the  tract  by  use  of  the 
volumes  given  in  Tables  V-VIII  in  the  Appendix,  or  any 
other  tables  based  on  D.B.H.  and  total  heights  that  would  be 
applicable  to  the  conditions.  Use  Form  4  for  recording  the 
measurements. 

(e)  Spaulding  rule  method. 

Tally  the  D.B.H.  inside  the  bark  and  the  length  of  all 
trees  on  the  tract  from  the  breast  height  point  to  a  point  on 
the  bole  where  the  D.B.H.  is  equal  to  h  D.B.H.  (outside 
bark).  Measure  this  length  by  means  of  a  hypsometer. 
Compute  the  volume  of  the  tract  by  the  Spaulding  rule  of 
thumb  explained  in  Problem  15,  Illustration  1,  Method  I. 
Use  Form  3  A. 


CRUISING  WITHOUT  THE  AID  OF  A  VOLUME  TABLE        47 

D.  References. — Numbers  14,  56,  58  and  60. 

E.  Discussion. 

1.  Which  method  is  most  accurate? 

2.  Which  method  is  the  most  rapid? 

3.  Which  method  would  you  choose  to  cruise  a  given  tract?     Why? 

4.  Can  the  first  two  methods  be  safely  used  by  inexperienced  men? 

PROBLEM    23.     (Field    and    Office.)     Cruising    Without    the    Aid    of    a 
Volume  Table. 

Explanation:  The  object  of  this  problem  is  to  illustrate  a  method  of  cruising 
a  large  tract  of  timber  when  there  are  no  volume  tables  available. 

Directions  : 

A.  Equipment  Required. 

1  Forest  Service  staff  compass,  or  hand  compass  when  the  former  is  not 

available. 
1  pair  of  tree  caHpers. 
1  field  notebook  with  Forms  3  A  and  B. 

B.  Parties  and  Organization. 

Men  will  be  organized  in  two-man  parties,  one  man  acting  as  compass- 
and  tallyman  and  the  other  as  caliperman.  Each  crew  will  cruise  a 
quarter  section  tract.  One  man  will  act  as  cruiser  and  the  other  as 
compassman  on  the  first  eighty  acres  covered,  and  the  second  man  as 
cruiser  for  the  second  eighty.  In  this  way  each  man  will  cruise  one-half 
of  the  tract.  The  men  should  assist  each  other  in  working  up  the  data, 
but  each  will  hand  in  only  the  data  for  the  area  he  has  cruised. 

C.  Method  of  Procedure. 

The  estimate  will  be  obtained  by  running  two  strips,  four  rods  wide, 
through  each  ''forty";  on  each  strip  diameters  breast  high  of  trees  10 
inches  and  over  will  be  tallied;  the  heights  will  be  obtained  from  a  height 
curve  constructed  from  data  collected  in  the  field  as  suggested  under 
Section  II;  the  volumes  will  be  computed  by  means  of  the  Spaulding 
Rule  of  Thumb. 

Part  I.  Running  the  Strips 

The  compassman  will  pace,  run  the  compass  line,  and  tally  the  sizes  called  off 
by  the  cruiser  who  will  take  the  D.B.H.  to  the  nearest  even  inch  of  all  trees  10 
inches  and  over  on  the  four- rod  strip. 

The  cruiser  should  be  careful  to  look  out  for  defects  in  the  trees  calipered. 
As  he  approaches  a  tree  when  at  a  distance  from  it  where  he  can  see  the  whole 
stem,  he  should  look  up  the  hole  for  conk,  fungus  or  other  defects.     The  volumes 


48  DETERMINATION  OF  THE  CONTENTS   OF   STANDS 

of  trees  showing  eonk  should  bo  discounted  by  reducing  the  sound  volume  50,  75 
or  100  per  cent,  according  to  the  cruiser's  judgment  as, to  the  extent  of  the  fungus 
attack.  Trees  with  other  defects  such  as  fire-scars,  hollow  butts,  broken  tops  or 
any  other  visible  defects  should  be  reduced  in  volume  by  the  proper  percentage 
estimated  in  the  field  for  each  tree  tallied.  All  snags  which  have  not  been  dead 
over  four  years  and  are  apparently  sound  should  be  tallied.  All  windfalls  which 
originally  stood  upon  the  strip  and  which  are  sound  enough  to  produce  lumber 
should  be  tallied.  In  this  respect  it  should  be  remembered  that  cedar  remains 
sound  for  a  great  many  years  and  that  cedar  windfalls  can  hence  be  taken  much 
more  closely  than  any  other  species.  The  taper  of  swell -butted  cedars  must  be 
taken  into  account  by  reducing  the  D.B.H.  several  inches  so  as  to  give  the  cedar  no 
more  swollen  butts  than  normal  fir  trees,  as  otherwise  the  Spaulding  rule  will  give 
too  high  volumes.  Defects  such  as  pitch,  spike  tops,  butt  rot,  shake,  and  all 
other  hidden  defects  and  breakage  will  be  discounted  by  deducting  a  lump  per- 
centage from  the  total  volume  at  the  end  of  work.  This  percentage  should  be 
estimated  by  the  cruiser  in  the  field.  Instructions  for  making  discounts  for 
defects  must  be  given  by  the  instructor  on  the  ground.  Special  directions  cannot 
be  given  here. 

For  tallying,  the  cruising  sheet  (Form  3  A)  will  be  used  which  has  the  page 
divided  into  columns  for  different  species.  One  column  will  be  used  for  tallying 
each  species  by  means  of  the  regular  dot  system  as  follows :  The  trees  are  tallied 
by  dots  and  lines,  in  blocks  of  ten,  as  indicated  in  the  following  table,  which  shows 
the  marks  corresponding  to  different  numbers, 


3.3456  -7  89  10 

'**:::  r.  n  n  n  0  K 


Dead  trees  or  snags  which  have  merchantable  contents  should  be  tallied  in  the 
same  column  with  the  living  trees  with  an  "x"  instead  of  a  dot  to  distinguish 
them.  Defective  living  trees  should  be  tallied  in  the  same  columns  with  the  sound, 
but  should  be  kept  separate  by  tallying  them  with  the  following  symbols: 

For  10  per  cent  deducted  from  the  sound  volume:  Q 

For  25  per  cent  deducted  from  the  sound  volume:  r\ 

For  50  per  cent  deducted  from  the  sound  volume:  J) 

For/75  per.  cent  deducted  from  the  sound  volume:  ^^ 

For  a  tree  tallied  by  mistake:  0 

Dead  defective  trees  should  be  tallied  in  a  similar  way,  except  that  an  "x" 
will  be  used  in  place  of  the  dot.  The  number  of  snags  over  12  inches  in  diameter 
without  merchantable  contents  may  be  tallied  in  the  column  provided  on  the 
right  hand  side  of  the  sheet  should  the  purpose  of  the  cruise  require  these  data. 
The  percentage  of  estimated  hidden  defect  for  each  species  and  the  breakage  for 
the  whole  "forty  "  should  be  tallied  in  the  proper  spaces  at  the  bottom  of  the  sheet. 


CRUISING  WITHOUT  THE  AID  OF  A  VOLUME  TABLE        49 

Each  forty  cruised  will  be  taUied  on  a  separate  sheet,  and  the  tallyman  should 
hence  change  sheets  when  a  forty  has  been  completed,  taking  care  that  the  forty 
number,  section  number,  and  direction  of  course  at  the  top  and  in  the  lower  right- 
hand  corner  of  the  tally  sheet  are  completely  filled  out  so  that  the  forty  can 
always  be  located.     The  different  species  will  be  tallied  in  separate  columns. 

Part  II.  Securing  the  Height  Data 

Since  heights  will  not  be  tallied  in  the  field  it  will  be  necessary  to  construct  a 
height  curve  from  data  collected  for  each  species.  For  this  purpose  sufficient 
time  should  be  taken  during  the  cruising  to  obtain  the  necessary  measurements. 
These  measurements  are  made  on  down  trees  and  as  many  should  be  taken  as 
possible.  For  each  down  tree  measure  the  D.B.H.  outside  of  bark,  width  of 
bark  at  D.B.H.  or  as  near  this  point  as  possible,  and  the  merchantable  length 
from  stump  to  ^  D.B.H.  outside  bark. 

Part  III.  The  Forest  Description 

While  running  the  strips,  or  at  any  other  convenient  time,  the  cruiser  should 
take  notes  to  be  used  as  a  basis  in  writing  a  detailed  forest  description  of  the  tract. 
Use  Form  3  B.    All  information  called  for  on  the  form  should  be  obtained. 

Part  IV.  Office  Computations 

The  estimate  will  be  worked  up  and  totaled  by  40-acre  tracts.  The  volume  of 
all  trees  above  22  inches  D.B.H.  except  hemlock  will  be  computed  in  feet  B.M. 
by  the  method  explained  in  Problem  15,  Illustration  1,  Method  II.  Hemlock 
16  inches  D.B.H.  and  over  will  be  computed  in  feet  B.M.  All  fir  from  16  inches 
to  22  inches  D.B.H.  inclusive  wih  be  computed  as  pihng,  and  all  cedar  from 
10  inches  to  22  inches  as  poles,  by  cimply  noting  the  number  of  pieces.  All  fir 
and  hemlock  from  10  inches  to  14  inches  D.B.H.  inclusive  will  be  computed  in 
ties.  This  will  necessitate  an  estimate  of  how  many  No.  1  ties  (6"X8"X8')  or 
No.  2  ties  (6"X6"X8')  an  average  10-,  12-  or  14-inch  tree  will  contain. 

The  following  data  should  be  handed  in  by  each  party: 

(1)  A  height  curve  and  a  volume  curve  both  on  D.B.H.  for  each  species, 

together  with  the  accompanying  tables  read  from  them. 

(2)  All  tally  sheets. 

(3)  Summary  sheet,  showing  the  cruise  by  species  for  each  forty  and  totals 

for  the  tract. 

(4)  A  forest  description  of  each  eighty.     Arrange  all  in  neat,  logical  order. 

D.  Reference. — Number  56. 


50  DETERMINATION  OF  THE  CONTENTS  OF  STANDS 

Note. — This  page  should  be  used  for  noting  special  instructions,   relating  to  the  pre- 
ceding exercise,  in  order  to  meet  the  conditions  of  a  particular  tract  or  region. 


CRUISING  WITH  THE  AID  OF  A  VOLUME  TABLE  51 

PROBLEM  24.     (Field  and  Office.)     Cruising  with  the  Aid  of  a  Volume 

Table.* 

ExPLAN.\TiON :  The  object  of  this  problem  is  to  illustrate  a  method  of  cruising  a 
tract  of  considerable  size  with  volume  tables  showing  values  for  trees  of  differ- 
ent diameters  and  total  heights. 

DiRECTIOX.S: 

A.  Equipment  Required. 

1  hand  compass  or  Forest  Service  Compass  and  Staff. 

1  pair  of  tree  caUpers. 

1  hypsometer. 

1  field  notebook  with  cruising  Forms  4  A  and  B. 

B.  Parlies  and  Organization. 

The  same  organization  as  outlined  for  Problem  23  will  be  followed  in 
this  exercise. 

C.  Method  of  Procedure. 

The  estimate  will  be  obtained  by  running  four  strips  four  rods  wide 
through  each  forty.  On  each  strip  the  diameters  breast  high  and  the 
total  heights  of  all  trees  10  inches  and  over  in  diameter  will  be  tallied. 
The  volumes  will  be  obtained  by  means  of  the  volume  tables  given  in  the 
Appendix  or  any  other  tables  based  on  diameters  breast  high  and  total 
heights,  applicable  to  the  conditions. 

Part  I.  Running  Strips 

The  compassman  will  pace,  run  the  compass  line  and  at  the  end  of  each  acre. 
(4  rods  wide  by  40  rods  long)  cruised  will  see  that  the  cruiser  changes  the  tally 
sheets.  If  the  object  of  the  work  requires  a  topographic  map  the  compassman 
will  make  such  a  map  while  the  cruiser  tallies  the  trees.  If  no  topographic  map  is 
required  he  need  only  run  the  compass  line  and  pace  the  distances  unless  the  area 
of  the  stand  be  irregular  in  which  case  he  should  plat  a  diagram  to  scale  on  Form  I 
of  the  field  notebook  showing  the  shape  of  the  tract,  boundaries  of  the  timber, 
limits  of  forest  types,  location  of  burns  or  other  features  affecting  the  forest  cover. 

The  cruiser  will  tally  the  diameters  breast  high  and  total  heights  of  all  trees 
10  inches  and  over  in  diameter.  At  the  end  of  each  acre  he  will  carefully  fill  out 
on  the  reverse  side  of  the  tally  sheet  the  acre  number,  direction  of  course,  section 
number,  etc.,  which  will  locate  the  acre,  and  he  will  then  change  tally  sheets. 

Tallying  will  be  done  on  Form  4  A,  using  the  thirty-foot  height  classification 
given  on  these  sheets,  i.e.,  up  to  75  feet,  75  to  105,  106  to  135,  136  to  165,  166  to 
195,  196  to  225,  226  to  255,  and  from  256  feet  up.     In  case  the  volume  table  used 

*  As  in  Problem  23,  this  exercise  will  need  to  be  modified  if  used  anywhere  except  in  the 
Pacific  Coast  region.  The  modifications  may  be  noted  on  the  blank  page  following  the 
problem. 


52 


DETERMINATION  OF  THE  CONTENTS  OF  STANDS 


is  constructed  with  a  diffcront  classification  of  heights  than  that  given  hero,  the 
same  height  classes  used  in  the  table  should  be  usetl  in  cruising.  The  dot  system 
of  tallying  described  in  the  previous  exercise  should  be  used.  Each  of  the  species 
will  be  talhed  separately  in  one  of  the  three  sets  of  columns  provided  on  the  tally 
sheets.  Should  more  than  three  species  be  found  on  the  area  to  be  cruised  the 
three  species  found  in  greatest  number  should  be  tallied  in  the  columns  provided 
and  other  species  tallied  at  the  bottom  of  the  sheet  by  name  and  size,  i.e.,  a  white 
pine  35  inches  D.B.H.  125  feet  high  would  be  tallied  W.  P.  -35  -125,  or  if  it  had 
10  per  cent  defect,  W.  P.  -35  -125  -10  per  cent. 

Deductions  for  all  defects  which  would  affect  the  amount  of  lumber  which 
can  be  cut  from  the  tree,  will  be  made  exactly  as  outhned  in  Problem  23,  except 
that  the  diameters  of  swollen-butted  cedars  need  not  be  reduced  unless  thesweUing 
is  excessive. 

Part  II.  Office  Computations 

After  completing  the  field  work  the  next  step  is  to  compute  the  contents  in 
board  feet  of  each  species  on  each  tally  sheet.  If  a  considerable  amount  of  this 
kind  of  work  has  to  be  done  a  multiplication  volume  table  should  be  made. 
This  is  made  by  expanding  the  volume  table  so  that  it  will  show  for  each  different 
D.B.H.  and  height  class  the  volumes  of  trees  from  one  to  ten  in  number.  For 
example,  Volume  Table  Number  V  in  the  Appendix  if  converted  into  a  multipli- 
cation volume  table  would  have  the  following  form : 


D.B.H. 


10 

12 

Etc. 


to  75 

76-105 

1 

2 

Etc.,  to 

1 

2 

3 

Etc.,  to 

tree 

trees 

10  trees 

tree 

trees 

trees 

10  trees 

80 

160 

100 

200 

300 

100 

200 

140 

280 

420 

Etc. 


With  such  a  table  the  volume  of  any  number  of  trees  up  to  ten  may  be  read 
off  at  a  glance  or  the  volume  of  any  other  number  of  trees  secured  by  a  short 
computation  and  the  work  will  be  much  hastened;  i.e.,  the  volume  of  13  trees 
would  be  the  sum  of  the  volume  of  10  trees  and  3  trees. 

Using  the  multij^lication  volume  table  one  man  should  call  off  the  number  of 
trees  in  each  D.B.H. -height  class  of  a  certain  species  to  the  other  man  of  his 
party  who  will  immediately  give  him  their  volume  as  read  from  the  table.  The 
first  man  will  enter  this  volume  on  the  tally  sheet  and  total  for  each  species,  or 
better  still  will  enter  the  volumes,  as  called  out,  in  an  adding  machine  and  secure 
the  total  with  the  machine.  The  totals  for  each  species  should  be  entered  at  the 
foot  of  the  proper  column  and  sliould  be  kept  separate  for  the  sound  live  trees,  the 
defective  live  trees,  and  the  sound  and  defective  dead  trees.  In  the  case  of  the 
defective  trees  the  totals  should  have  defect  properly  discoimted. 


CRUISING   WITH   THE   AID   OF  A  VOLUME   TABLE  53 

Each  distinct  total  for  oach  species  should  then  be  multiplied  bj'  5,  since  the 
strips  tallied  covered  20  per  cent  of  the  total  area.  These  totals  should  then  be 
reduced  by  the  percentage  estimated  in  the  field  for  hidden  defect  and  breakage. 
The  total  of  each  species  and  the  grand  total  of  all  species  for  each  forty  should 
then  be  computed  by  adding  together  the  totals  on  each  tally  sheet  included  in 
the  forty. 

Should  any  acre  tallied  be  of  full  size  but  the  tract  it  represents  of  irregular 
size,  the  area  of  the  fractional  tract  should  be  obtained  before  the  estimate  is 
calculated.  This  can  be  done  with  a  planimeter  by  measuring  the  plat  made  in 
the  field,  or  by  estimating  the  number  of  squares  on  the  plat  included  in  the 
irregular  tract  and  calculating  their  equivalent  area.  The  volume  of  this  tract 
is  then  secured  by  multiplying  the  volume  of  the  acre  tallied  by  the  number  of 
acres  in  the  irregular  tract.  For  example,  in  a  20  per  cent  cruise  each  acre 
talhed  represents  5  acres  and  the  total  cruise  were  the  area  perfectlj^  regular, 
would  be  secured  by  multiplying  the  volume  of  the  acre  tallied  by  5.  Suppose, 
however,  that  one  cornev  of  the  tract  is  logged  ofT  and  from  the  plat  it  is  found 
that  2  acres  contain  no  timber.  The  volume  of  the  acre  sheet  would  then  be 
multiplied  by  3  instead  of  5. 

If  neither  the  acre  tallied  nor  the  tract  it  represents  were  complete  the 
volume  of  the  equivalent  full  acre  should  be  found  by  dividing  the  volume  of  the 
fractional  acre  by  its  area  expressed  in  tenths  of  an  acre.  The  volume  of  the 
fractional  tract  would  then  be  found  as  explained  above.  For  example,  the  last 
tally  sheet  coveis  but  0.8  of  an  acre  and  it  represents  but  3  acres  instead  of  5  as 
normally.  The  volume  of  the  fractional  acre  would  then  be  divided  by  0.8  to 
reduce  the  fractional  acre  to  terms  of  a  whole  acre.  This  volume  would  then  be 
multii^lied  by  3  to  find  the  volume  of  the  tract.  The  same  method  might  also 
be  applied  to  the  forty  as  a  unit  instead  of  the  acre. 

Each  party,  upon  the  completion  of  the  work,  should  hand  in  all  tally  sheets 
and  a  summary  sheet  showing  the  total  stand  by  species  for  each  forty  and  the 
grand  total  for  the  whole  area. 

D.  References.— lumbers  37,  55,  57,  59,  61  and  63. 

E.  Discussion. 

1.  How  would  the  method  of  procedure  outlined  above  be  modified  if 

the  volume  tables  to  be  used  were  based  upon  merchantable  lengths 
instead  of  total  heights? 

2.  How  would  the  method  of  procedure  be  modified  if  the  heights  of  the 

individual  trees  were  not  tallied  but  the  trees  on  each  forty  were 
given  one  of  three  height  classifications  and  the  volume  tables  used 
were  constructed  with  similar  height  classifications. 

3.  Discuss  the  respective  merits  of  deducting  for  defect  by  a  percentage 

for  each  individual  tree  or  by  a  lump  percentage  to  cover  all  defects 
for  each  acre  cruised. 

4.  What  is  the  advantage  in  changing  tally  sheets  at  the  end  of  each  acre 

rather  than  at  the  end  of  each  forty? 


54  DETERMINATION  OF  THE  CONTENTS  OF  STANDS 

5.  Discuss  llio  advanlagos  aiul  disadvantasos  of  using  a  correction  factor 

to  adapt  the  cruise  to  stands  outside  of  the  strip  cruised  whi(;h  have 
a  greater  or  a  lesser  vohmie  per  acre  than  the  stand  on  the  strip. 

6.  What  criticisms  of  the  method  of  procedure  given  above  for  carrying 

on  the  office  work  might  be  made  and  why? 


CRUISING   WITH   THE   AID   OF   A   VOLUME   TABLE  55 

Note. — This   page   should    be    used    for    noting   special    instructions   to   be   given  by   the 
instructor  in  order  to  meet  the  conditions  of  a  particular  tract  or  region. 


SECTION  VIII— GENERAL  GROWTH  STUDIES 

Explanation. — Studies  in  the  growth  of  trees  are  made  chiefly  for  the  pur- 
pose of  determining  the  number  of  years  required  for  trees  to  become  mer- 
chantable in  size,  for  the  prediction  of  future  yield  in  volume,  as  a  basis  for 
silvicultural  practice  and  as  steps  in  organizing  forests  for  continuous  timber 
production.  Studies  are  made  on  growth  in  diameter,  height,  basal  area, 
and  volume.  These  may  be  made  for  individual  trees  or  as  an  average  for 
small  groups  or  even  for  extensive  areas.  As  a  basis  for  predicting  the  vol- 
ume growth  of  stands  studies  are  usually  made  in  terms  per  acre  and  are 
then  known  as  yield  studies.  Growth  in  diameter  and  height  form  the 
direct  basis  for  the  volume  and  yield  studies. 

In  many  studies  it  is  necessary  to  distinguish  growth  with  reference  to 
time.  Thus  we  have  (C.  A.  G.)  Current  Annual  Growth,  that  for  any  one 
specific  year;  (M.  A.  G.)  Mean  Annual  Growth,  the  average  annual  rate  of 
growth  during  the  life  of  the  tree;  the  (P.  G.)  Periodic  Growth,  the  rate  for 
any  specific  period  of  years.  In  some  problems,  particularly  the  prediction 
of  growth  in  the  future,  we  have  growth  per  cent,  which  is  determined  by 
means  of  a  simple  interest  formula  that  shows  the  per  cent  of  increase  in 
relation  to  the  present  size  of  the  tree  or  stand. 

Prerequisite  Study. — Before  taking  up  the  exercises  included  in  this  section 
the  student  should  review  the  general  method  of  collecting  data  for  growth 
studies,  Problem  7. 

Caution. — In  all  growth  studies  it  should  be  remembered  that  the  number  of 
measurements  required  both  as  to  kind  and  quantity  will  vary  with  the 
specific  problem  to  be  solved.  Since  separate  studies  must  be  made  for 
trees  growing  under  different  conditions,  a  completed  curve  or  table  will 
have  no  value  unless  it  is  labeled  with  all  the  conditions  of  growth.  This  is 
even  more  important  in  growth  studies  than  in  volume  studies.  All  of  the 
points  enumerated  in  the  outline  below  should  be  considered  in  the  title  or 
label  for  each  distinct  growth  study,  though  not  all  need  be  included  because 
some  conditions  may  be  wholly  obvious  from  some  others  already  stated. 
For  example,  if  a  study  had  been  made  of  the  growth  of  Virgin  Yellow  Pine 
in  Eastern  Oregon,  it  would  be  practically  obvious  that  it  represents  the 
growth  in  an  uneven-aged  stand. 

Points  to  he  Considered  in  Connection  with  Title.* 

1.  The  general  problem. 

2.  Species. 

*  Those  italicized  should  appear  in  the  title  of  each  problem. 
56 


DETERMINATION  OF  THE  TOTAL  AGES  OF  TREES    57 

3.  Even-  or  uneven-aged  stand. 

4.  Pure  or  mixed  stand. 

5.  Forest  type. 

6.  Soil  or  site  quality. 

7.  Density. 

8.  Number  of  trees  upon  which  the  study  is  based. 

9.  Locality. 

10.  Virgin  or  second  growth. 

11.  Date. 

12.  Be  sure  to  indicate  units  of  measurement  (feet,  inches,  B.M.,  etc.)  and 

kind  of  growth  (Dia.,  Vol.,  P.  A.  G.,  C.  A.  G.,  etc.)  on  all  curves  and 
tables, 

PROBLEM  25.     (Field.)     The  Determination  of  the  Total  Ages  of  Trees. 

Explanation. — In  this  problem  it  is  assumed  that  we  have  determined  the 
ages  at  the  stump  of  a  large  number  of  trees.  In  order  to  determine  the 
total  ages  of  these  trees  it  would  be  necessary  to  cut  the  trees  near  the  sur- 
face of  the  ground  because  that  is  the  only  portion  where  a  growth  ring  has 
been  added  each  year  from  the  time  the  tree  was  a  one  year  old  seedling, 
several  inches  high,  to  the  time  of  cutting.  To  cut  large  trees  near  the  sur- 
face of  the  ground  would,  of  course,  be  impracticable.  Hence  the  ages  at  the 
stumps  must  be  corrected  by  a  separate  study  of  height  growth  on  seedlings 
whose  total  heights  vary  about  as  the  stump  heights. 

Illustration. — To  determine  the  total  ages  of  the  trees  analyzed  in  Prob- 
lem 7. 

Directions: 

A.  Parties. — Each  student  can  work  to  advantage  by  himself. 

B.  Equipment. 

1  sharp  pocket  knife. 

1  rule  or  tape  graduated  to  inches. 

1  hand  lens. 

Pencil  and  field  notebook  with  Form  1. 

C.  Method  of  Procedure. 

1.  Select  trees  of  the  same  species  and  of  about  the  heights  of  the  stumps 

and  under  the  same  conditions  of  growth  as  those  whose  total  ages 
it  is  desired  to  find. 

2.  With  the  pocket  knife  cut  from  10  to  15  seedlings  at  about  one  inch 

from  the  surface  of  the  ground.     The  heights  should  vary  about  as 
the  heights  of  the  stumps  of  the  trees  whose  ages  are  to  be  corrected. 

3.  Determine  the  age  and  height  of  each.     In  conifers  this  may  be  done 

by  countmg  the  whorls  of  branches  and  checking  by  ring  counts: 


58  GENERAL  GROWTH  OF  STUDIES 

in  hardwoods  usually  ring  counts  alono  can  be  used,  though  often 
these  may  be  checked  by  the  annual  nodes,  or  terminal  bud  scars. 
Record  the  measurements  in  a  table  of  two  columns  with  ages 
opposite  heights. 

Note. — When  the  annual  nodes  are  conspicuous  it  is  often  possible  to  obtain  a  number 
of  height  measurements  from  each  individual  seedling  as  follows: 

1.  After  the  total  age  and  the  total  height  of  a  seedling  are  determined,  subtract  one 

from  the  total  age  and  measure  the  height  to  the  first  annual  node  below  the  tip. 

2.  In  a  similar  manner  determine  the  values  with  reference  to  each  of  the  remaining 

annual  nodes. 
(The  same  may  be  done  by  cutting  the  seedlings  into  6-inch  lengths  and  constructing 
a  height  growth  table.     See  Problem  29.) 

4.  On  a  sheet  of  cross-section  paper  (Form  1  of  Field  Notebook)  lay  otT 

heights  as  abscissae,  and  ages  as  ordinates.  Plot  the  values,  in 
half-foot  height  classes,  draw  a  smooth  curve  and  read  off  a  table 
showing  the  average  ages  of  the  heights  for  each  0.5  of  a  foot,  and 
label. 

5.  Apply  this  table  directly  to  the  stump  ages  as  follows,  and  record  in 

the  proper  spaces  in  the  data  blanks, 
(a)  Look  up  the  stump  height  of  each  tree  on  the  front  of  the  Analysis 

Blank  (Form  2  A). 
(6)  Determine  in  the  table  just  constructed  the  number  of  years  it 

took  the  tree  to  grow  to  stump  height. 
(c)  Add  this  number  of  years  to  the  age  at  the  stump  and  record  as 

''Total  Age." 

PROBLEM  26.     (Office.)     The  Determination  of  Diameter  Growth  in  Fjver)- 
aged  Stands. 

Explanation. — The  object  of  this  exercise  is  to  ilhistrate  the  fundamental 
principles  involved  in  all  diameter  growth  studies  in  even-aged  stands.  In  all 
cases  tables  are  to  be  prepared  that  will  show  the  average  diameter  a  tree 
may  be  expected  to  attain  at  some  one  or  more  points  (certain  prescribed 
distances  above  the  ground)  along  the  bole  of  the  tree.  The  growth  at  each 
of  these  points  is  determined  by  a  separate  study.     The  method  of  procedure 

.  will  be  practically  the  same  for  all  problems  involving  diameter  growth  in 
even-aged  stands,  as  that  outlined  in  the  illustration  given  below.  It  is  cus- 
tomary to  make  these  studies  in  ten-year  age-periods. 

Illustration. — To  Construct  a  Table  of  Average  Diameter  Growth  at  the 
Stump  for  Even-aged  Stands,  not  Thinned. 

A.  Data  Required. — Stump  analysis  and  total  ages.     Use  Data  Series  III. 

B.  Method. — Plotting  the  values  before  averaging. 

Note. — When  this  problem  is  completed  do  not  erase  any  of  the  plotted  points. 
They  will  be  of  use  in  succeeding  problems.     When  these  data  are  not  to  be  used 


DIAMETER   GROWTH   IN   EVEN-AGED   STANDS  59 

for  other  purposes  it  may  be  more  convenient  to  average  before  plotting,  especially 
when  a  large  number  of  trees  are  used.  In  this  case  rule  a  large  sheet  of  paper  so 
that  there  will  be  one  vertical  column  for  each  age  from  one  year  to  the  age  of  the 
oldest  tree.  Record  the  radius  measurements  in  their  proper  age  columns,  average 
and  finally  even  off  by  means  of  a  curve. 

Method  of  Procedure.— (Using  method  of  plotting  before  averaging.) 

1.  Ages  in  this  case  are  the  independent  variables,  diameters  the  depend- 

ent variables;  hence,  lay  off  the  cross-section  paper  with  ages  ui 
ten-year  periods  on  the  abscissa  axis,  and  diameters  in  inches  on  the 
ordinate  axis.     Label. 

2.  Before  plotting  the  values  from  any  analysis  sheet  it  should  be  checked 

according  to  the  instructions  for  the  tallyman,  Problem  7.  If  it 
does  not  check  do  not  use  it.  All  data  in  this  book  supplied  for  use 
with  this  problem  have  been  checked. 

3.  Determine  the  respective  values  of  the  points  to  be  plotted  as  follows, 

and  plot  them  accordingly : 

(a)  The  successive  diameter  values  by  multiplying  the  radius  measure- 
ments, as  recorded,  by  2. 

(6)  The  age  corresponding  to  the  first  radius  measurement  is  taken  as 
recorded  in  the  upper  left-hand  corner  of  the  space  allotted  to 
the  first  decade.  The  succeeding  ages  are  determined  by  adding 
10  years  to  the  age  of  the  first  decade  for  the  age  of  the  second 
decade,  and  10  years  more  for  each  successive  decade;  or  the 
age  at  any  decade  is  equal  to:  [(No.  of  the  decade  minus  1) 
times  10]  plus  number  of  years  in  the  first  decade.  This, 
however,  gives  the  age  at  the  stump  and  not  the  total  age  of 
the  tree;  hence,  in  order  that  our  study  may  be  based  on  the 
total  age,  it  will  be  necessary  to  add  also  the  number  of  years  it 
took  the  tree  to  grow  to  stump  height.  The  formula  then 
becomes:  The  total  age  for  any  decade  measurement  equals 
[(No.  of  the  decade  minus  1)  times  10]  phis  the  number  of  years 
in  first  decade  plus  the  number  of  years  required  to  grow  to 
stump  height.  During  the  actual  process  of  plotting  it  is  neces- 
sary to  determine  this  value  only  for  the  first  point  to  be 
plotted.  The  values  (ages)  of  the  succeeding  abscissae  can  be 
determined  very  rapidly  by  simply  adding  ten  years  to  each 
preceding  value. 

4.  When  all  the  values  are  plotted  average  for  each  ten-year  period  as 

follows : 
(a)  The   average   ages:     By   averaging   separatelj',    in   a   horizontal 

direction,   all  plotted  points  in  each  ten-year  period,  letting 

0  to  10  inclusive  represent  the  first  period,  10.1  to  20  inclusive 

the  second,  and  so  on. 
(h)  The  average  diameter:    By  averaging  separately,  in  a  vertical 

direction,  all  points  in  each  age  period  as  in  (a). 


60  GENERAL  GROWTH  OF  STUDIES 

5.  Draw  a  smooth  curve  and  read  off  a  table  showing  the  average 

diameters  at  the  end  of  each  ten-year  period. 

6.  Label. 

PROBLEM  27.     (Office.)     The  Determination  of  Growth  in  Uneven-aged 
Stands. 

Explanation. — Growth  in  uneven-  or  many-aged  stands  differs  from  growth 
in  even-aged  stands  in  that  the  individual  trees  grow  more  nearly  like  the 
trees  of  a  certain  diameter  than  they  do  like  trees  of  a  certain  age.  Hence, 
except  when  it  is  desired  to  determine  the  mean  annual  growth  of  trees, 
growth  studies  in  uneven  aged  stands  are  usually  based  on  diameters  (D.B.H.) 
instead  of  ages.  This  holds  true  and,  as  described  below,  is  applicable  to  all 
kinds  of  growth  in  uneven-aged  stands.  The  object,  then,  is  to  determine 
how  fast  a  tree  of  a  certain  diameter  is  growing,  either  in  diameter,  height, 
volume,  or  other  dimensions.  This  immediately  makes  it  evident  that 
when  a  tree  of  one  diameter  class  has  grown  to  the  next  higher  diameter 
class  it  has  a  different  rate  of  growth.  Our  problem  then  becomes  one  of 
determining  first  of  all  the  periodic  annual  growth  for  each  diameter  class 
and  from  this  the  number  of  years  required  to  grow  one  unit;  i.e.,  in  diam- 
eter, one  inch. 

The  independent  variables,  then,  will  be  diameters  breast  high,  and  the 
dependent  variables,  periodic  growth  as  determined  in  5-  or  10-year  periods. 
Unless  there  is  some  special  reason  for  determining  the  mean  annual  growth 
use  periodic  growth  on  D.B.H.  for  all  problems  in  mamj-  (or  uneven-)  aged 
stands. 

Illustration. — To  Construct  a  Table  of  Diameter  Growth  at  the  Stump  for 
Uneven-aged  Stands,  Based  on  D.B.H. 

Directions: 

A.  Data  Required. — The  D.B.H.  and  measurements  of  the  last  10  rings  at 

the  stump,  or  at  D.B.H. 

Note. — The  data  for  this  problem  can  be  obtained  at  D.B.H.  from  standing  trees  with 
the  increment  borer,  but  usually  more  satisfactory  work  can  be  done  on  felled  trees  in  con- 
nection with  a  logging  operation.  The  data  supplied  for  this  exercise  were  obtained  in  the 
latter  manner.  Use  Scries  II.  The  data  in  this  series  are  somewhat  limited  for  the 
purpose  but  show  admirably  what  a  small  variation  enters  into  the  final  results  even  with 
limited  data.  Compare  the  results  obtained  under  "  D  "  of  this  problem  as  worked  out  by 
different  members  of  the  class.  The  problem  also  illustrates  the  need  for  a  large  number 
of  data  for  absolute  accuracy  in  all  problems  dealing  with  averages. 

B.  Method. — Averaging  before  plotting. 

C.  Method  of  Procedure. 

1.  Group  all  trees  into  1-inch  D.B.H.  classes  {e.g.  8-inch  class  7.6-8.5, 
inclusive) , 


DIAMETER  GROWTH  AT   THE  STUMP  61 

2.  Average  the  periodic  growth  and  the  diameter  class  of  all  trees  of 

each  class  separately.     (See  Problem  16  for  method.) 

3.  Even  off  by  a  curve. 

4.  Construct  a  table  showing  for  each  D.B.H.  inch  class: 

(a)  The  periodic  growth  as  read  from  the  table. 

(b)  The  periodic  annual  growth. 

(c)  The  number  of  years  required  to  grow  1  inch. 

D.  Discussion. 

1.  Solve  the  following  problem  from  the  above  table: 

If  you  are  cutting  to  a  14-inch  diameter  limit,  in  how  many  years 
will  the  8-inch  trees  be  ready  to  cut?  Show  how  you  derived  the 
result. 

PROBLEM    28.     (Office.)     The    Transposing    of    a    Table    of    Diameter 
Growth  at  the  Stump  to  Growth  at  D.B.H. 

Explanation. — Since  for  practical  purposes  all  measurements  of  trees  are 
based  on  the  D.B.H.,  outside  of  bark,  the  most  valuable  diameter  growth 
tables  are  those  which  show  the  growth  at  that  point.  For  obvious  reasons 
it  is  in  most  cases  impracticable  to  analyze  trees  at  the  D.B.H.  The  object 
of  this  exercise  is  to  construct  a  table  showing  the  rate  of  growth  at  D.B.H, 
outside  of  bark  from  analyses  made  at  the  stump  (D.I.B.) 

Directions: 

A.  Data   Required. — D.B.H.,    complete   stump   analyses,    and   total   ages. 

Use  the  same  data  (Series  III)  used  in  Problem  26.  The  curve  for 
average  D.I.B.  growth  at  the  stump  constructed  in  that  exercise  will 
be  taken  as  a  basis  for  the  work. 

B.  Method  of  Procedure. 

1.  Lay  off  a  sheet  of  cross-section  paper  as  in  Problem  26,  and  transfer 

the  average  curve  from  that  sheet  to  the  new  sheet  by  plotting  the 
values  from  the  table  made  in  Problem  26.  Do  not  prick  the  points 
through  the  paper  as  this  often  results  in  inaccuracies.  Label  this, 
"Curve  I,  (D.I.B.  Stump)." 

2.  On  this  same  sheet  now  draw  Curve  II  to  show  the  ratio  between 

D.I.B.  (stump)  and  D.B.H.  (outside  of  bark)  as  follows: 
(a)  Let  ordinates  represent  D.I.B.  values  as  for  Curve  I.  Now  lay  off 
D.B.H.  values  as  abscissa),  the  abscissa)  to  have  the  same  value 
(in  number  of  spaces  on  the  paper  alotted  to  each  unit)  already 
established  for  the  ordinates;  i.e.,  if  one  large  space  represents 
2  inches  on  the  ordinate  axis,  it  shall  also  represent  2  inches  on 
the  abscissa  axis.  These  values  may  be  placed  directly  below 
the  age  figures.     Be  sure  to  label  each  set  of  figures.     Confusion 


62  GENERAL  GROWTH   OF  STUDIES 

may  often  be  avoided  by  using  a  distinct  color  for  all  points, 
curves,  figures,  and  labels  belonging  together. 

(6)  Plot  values  of  D.I.B.  (ordinates)  on  D.B.H.  (abscissa)  for  each 
tree  as  recorded  on  the  Tree  Measurement  Blank.  Select  the 
trees,  so  that  they  will  be  well  distributed  over  the  various 
diameters.  D.I.B.  values  can  be  obtained  from  Data  Series  III 
by  doubling  the  last  radius  measurement. 

(c)  Average;  draw  a  curve.  Label  this  "Curve  II  (Ratio  Curve)." 
It  may  cross  Curve  I. 

3.  These  two  curves  now  show  the  relationship  between  growth  at  D.I.B. 
•  (stump)  and  D.B.H.  on  age.     The  D.B.H.  for  any  age  may  be 

determined  as  follows: 

(a)  Beginning  on  the  abscissa  axis  at  the  desired  age,  trace  the  per- 
pendicular at  that  point  to  the  point  where  it  crosses  the  D.I.B. 
curve  (Curve  I). 

(6)  From  this  point  trace  the  horizontal  line  straight  across  to  the 
Ratio  Curve  (Curve  II).  The  line  dropped  from  this  point 
perpendicular  to  the  abscissa  axis  will  indicate  the  D.B.H.  for 
the  age  started  with.  Show  by  dotted  line  and  arrrows  on  the 
cross-section  sheet  how  this  reading  is  obtained. 

4.  It  is  customary  to  draw  a  third  curve  representing  growth  at  D.B.H. 

as  follows : 

(a)  On  the  same  sheet  of  cross-section  paper  let  ordinates  as  there 

laid  ofT  for  Curves  I  and  II  now  represent  D.B.H.,  and  ages  as 
established  for  Curve  I  abscissa;. 

(b)  From  Curves  I  and  II  read  off  the  values  of  D.B.H.  on  age  in 

10-year  periods,  as  explained  in  3,  (a)  and  (h),  and  plot  them 
according  to  4  (a) . 

(c)  Even  off  by  a  curve.     Call  this  Curve  III. 

5.  Read  off  two  tables. 

1.  Showing  the  diameters  (D.B.H.)  at  different  ages  in  10-year  periods. 

2.  Showing  ages  for  the  different  diameters  (D.B.H.)  in  even  inches. 

PROBLEM  29.     (Office.)     The  Determination  of  Height  Growth. 

Explanation. — The  determination  of  height  growth  depends  upon  the  prin- 
ciple that  the  number  of  annual  rings  at  any  point  along  the  bole  of  the  tree 
represents  the  number  of  years  it  took  the  tree  to  grow  from  that  point  to 
the  tip.  Thus  the  total  age  represents  the  number  of  years  it  took  the 
whole  tree  to  grow  from  the  ground  to  the  tip,  and  the  number  of  rings  at 
any  cross-cut  the  number  of  years  to  grow  from  that  point  to  the  tip.  In 
order  to  find  how  many  years  it  took  the  tree  to  grow  from  the  surface  of  the 
ground  to  any  point  intermediate  between  it  and  the  tip  subtract  the  number 
of  annual  rings  that  occur  at  the  desired  point  from  the  total  age. 

Illustration  1  —To  construct  ;i  T;i))lo  of  Ileighl  Growth  for  Eirn-df/cd  Stands. 


VOLUME  GROWTH   IN   AN    INDIVIDUAL   TREE  63 

Directions: 

A.  Data  Required. — Total  ages  and  ring  counts  (decade  measurements  not 

needed)  at  various  intervals  along  the  boles  of  the  trees,  recorded  with 
the  heights  above  the  surface  of  the  ground  at  which  the  counts  are 
made.  Whenever  height  growth  studies  are  made  in  connection  with 
some  study,  not  involving  complete  stem  analysis,  such  for  example,  as 
diameter  growth  at  the  stump,  it  is  necessary  to  make  ring  counts  at 
various  intervals  along  the  bole  for  the  height  determinations. 
Usually  a  good  height  growth  table  can  be  made  from  a  much  smaller 
number  of  trees  than  required  for  diameter  growth.     Use  data  Series  IV. 

B.  Method  of  Procedure. 

1.  Determine  which  is  the  independent  and  which  the  dependent  variable. 

Ask  the  instructor  if  you  are  right,  then  lay  off  the  cross-section 
paper  accordingly. 

2.  Determine  the  number  of  years  required  to  grow  to  the  height  of  the 

cross-cut  in  question  by  subtracting  the  number  of  rings  at  the 
various  cross-cuts  from  the  total  age. 

3.  Plot  the  values,  average,  and  read  off  the  proper  kind  of  table. 
Note  in  this  problem  the  value  of  plotted  points  for   interpolating 

values. 

Illustration  II. — To  Construct  a  Table  of  Height  Growth  for  Uneven,  or 
Many-aged  Stands,  Based  on  D.B.H. 

Explanation. — This  exercise  aims  to  throw  the  student  upon  his  own  responsi- 
bility  and  should  be  written  out  instead  of  being  worked  out. 

Directions. 

A.  Data. — Determine  first  what  data  (enumerating  all  measurements)  are 

required. 

B.  Method  of  Procedure. 

1.  Outline  the  method  step  by  step. 

Suggestion. — Take  into  consideration  the  fundamental  differences  in 
the  construction  of  growth  tables  in  even-  and  in  uneven-aged  stands 
as  illustrated  in  Problems  26  and  27,  and  apply  to  Height  Growth. 
Determine  first  which  is  dependent  and  which  independent  variable, 
and  whether  you  would  use  M.  A.  G.  or  Per.  G.  according  to  the  pro- 
cedure in  many-aged  stands.  If  you  have  any  difficulties  read  again 
the  Explanation  to  Problem  27. 

PROBLEM  30.  (Office.)  The  Determination  of  Volume  Growth  in  an 
Individual  Tree. 
Explanation. — Volume  growth  may  be  based  on  stem  analysis  data  or  on 
measurements  taken  on  a  large  number  of  standing  trees  of  different  ages. 
In  the  first  case  the  trees  are  analyzed  in  the  field  as  in  Problem  7  and  the 
volumes  of  the  trees  at  different  ages  are  reconstructed  from  the  analysis.  In 
the  second  case  average  trees  in  even-aged  stands  of  different  ages  are  meas- 


64 


GENERAL  GROWTH   OF  STUDIES 


ured  and  the  volumes  calculated  and  plotted.  The  object  of  this  problem 
is  to  illustrate  the  fundamental  principles  involved  in  all  volume  growth 
determinations  based  on  analyses.  In  the  different  problems  involved  slight 
modifications  are  of  course  necessary  in  the  method  of  collecting  data  and  in 
the  method  of  working  them  up  into  the  final  table.  These  will  be  empha- 
sized in  the  succeeding  problems.  The  underlying  principle  in  the  study  is 
to  reconstruct  each  tree  analyzed  on  the  basis  of  its  dimensions  10,  20,  etc., 
years  ago. 
Illustration. — To  Determine  the  Volume  Growth  of  an  Individual  Tree  in 
Cubic  Feet  and  in  Board  Feet,  Based  on  Age. 

A.  Data  Required. — Complete  stem  analysis.     Use  tree  number  116  in  Data 

Series  V. 

B.  Method  of  Procedure. 

1.  Calculate  the  volume  in  cubic  feet  without  bark  of  the  whole  stem  for 
each  10-year  period  in  the  life  of  the  tree,  using  Smalian's  formula 
for  contents  of  logs,  the  cylinder  formula  for  stumps,  and  the  cone 
formula  for  tips  above  the  last  log,  as  follows:  (Calculations  for 
5  to  7  ten-year  periods  will  illustrate  the  problem.) 
(a)  On  a  sheet  of  note  paper  arrange  a  blank  form  like  the  following. 
Preserve  all  calculations  on  this  form. 


Cross  Cut 


Diameter 

Inside  Bark, 

Inches 


Area, 
Square  Feet 


Section 


Length  of 
Section 


Volume, 
Cubic  Feet 


Volume, 
B.M. 


1 
2 
3 
4 
Etc. 


Stump 

1st  Log 

2d  Log 

Etc. 


Present  Time  (Give  Age) Total 

1 

Stump 

2 

1st  Log 

3 

2d  Log 

4 

Etc. 

Etc. 

Tree  10  Years  Ago  (Give  Age) Total  Volume. 


VOLUiME   GROWTH   IN   AN    INDIVIDUAL  TREE  65 

(b)  Calculate  the  volume  of  the  tree  according  to  its  present  dimen- 

sions by  calculating  the  volume  of  each  section  separately,  and 
add  all  of  them  for  total  volume.  The  dimensions  of  the  diam- 
eters may  be  determined  from  the  last  set  of  figures  recorded 
on  the  analysis  sheet,  for  each  section  analyzed.  As  they  are 
radius  measurements  they  should  be  doubled. 

(c)  In  a  similar  manner  calculate  the  volume  of  the  tree  by  recon- 

structing from  the  analysis  its  dimensions  at  10,  20,  30,  40  years 
ago  and  so  on  down  to  within  the  first  10-year  period  in  the  life 
of  the  tree.  (Make  only  5  to  7  calculations.)  The  diameters 
of  the  successive  10-year  periods  are  again  determined  from  the 
radius  measurements  recorded  on  the  analysis  sheet.  For  ten 
years  ago,  for  example,  the  radius  at  each  cross-section  will  be 
represented  by  the  next  to  the  last  series  of  radius  measure- 
ments; for  twenty  years  ago  by  the  third  from  the  last,  and  so 
on.  The  lengths  of  the  logs  or  sections  are  recorded  on  the 
front  of  the  analysis  sheet,  including  the  height  of  the  stump 
and  the  length  of  the  tip  of  the  present  tree.  The  lengths  of 
the  tips  of  the  reconstructed  trees,  however,  must  be  determined 
by  special  calculations,  because  the  tips  usually  end  somewhere 
between  the  last  cross-cut  and  the  original  tip,  or  between  two 
successive  cross-cuts. 
Determine  the  lengths  of  the  individual  tips  by  proportion  as 
follows : 

(1)  Determine  the  periodic  annual  height  growth  of  the  section 

above  the  last  log  in  the  reduced  tree  under  consideration 
by  dividing  the  length  of  the  section  by  the  number  of 
years  it  took  the  tree  to  gi-ow  that  length. 

(2)  Multiply  the  periodic  annual  height  growth  by  the  number 

of  rings  at  the  base  of  the  tip  whose  height  you  wish  to  find. 
If  the  tip  of  the  reduced  tree  happens  to  be  in  the  tip  of 
the  present  tree,  the  length  of  the  present  tip  divided  by 
the  number  of  rings  at  its  base  will  equal  the  periodic 
annual  height  growth.  If  the  tip  of  the  reconstructed 
tree  falls  within  any  of  the  sections  below  the  present  tip, 
the  total  number  of  rings  at  the  top  of  the  section  sub- 
tracted from  the  total  number  of  rings  at  the  bottom  of 
the  section  will  equal  the  number  of  years  it  took  the  tree 
to  grow  the  length  of  the  section.  Then  divide  the  length 
of  the  section  by  this  number  of  years,  as  just  determined, 
to  obtain  the  periodic  annual  growth  (P.  A.  G.)  in  height. 
Multiply  this  by  the  number  of  rings  at  the  base  oj  the  tip 
U'hose  height  it  is  desired  to  find. 

(d)  Determine  volume  of  tip  as  usual  B.A.X^H. 

(e)  Enter  the  volumes  of  the  separate  sections  of  each  reconstructed 


6G  GENERAL  CiKOWTH   OF   STUDIES 

tree  in  the  proper  place  on  the  blank  form  and  add  for  total 
volume. 
2.  Now  determine  the  rate  of  volume  growth  in  board  feel  in  a  similar 
manner  to  that  just  described,  except  as  follows: 
(a)  Use  only  the  merchantable  portion  of  the  stem,  assuming  -every- 
thing merchantable  above  the  stump  down  to  6  inches  D.I.B. 
at  the  top  of  the  log.     Tii)s  and  stumps,  of  course,  must  be 
omitted,  also  logs  whose  top  diameters  are  less  than  6  inches. 
(6)   Use  the  International  Log  Rule  as  worked  out  in  Problem  9  or  any 
other  rule  giving  values  down   to  6  inch  top  diameters,   for 
determining  the  board  foot  values. 

(c)  Record  the  values  in  their  proper  places  in  the  blank  forms,  and 

total. 

(d)  Make  a  final  table  showing  only  the  volume  in  cubic  feet  and  in 

board  feet  in  10-year  age  periods. 

C.  Discussion. 

1.  What  would  be  some  of  the  practical  applications  of  such  a  table. 

PROBLEM    3L     (Office.)     The    Determination    of    Volume    Growth    by 
Graves'  Modification  of  Mlodjianski's  Method. 

Explanation. — A  table  showing  growth  based  on  age  might  be  constructed 
from  analysis  data  by  first  calculating  the  volume  growth  of  each  individual 
tree  as  was  done  in  Problem  30,  and  averaging  the  results  to  determine  the 
average  rate  of  growth.  The  student  will  realize  fully  from  the  foregoing 
exercise  without  further  emphasis  the  tremendous  amount  of  work  necessary 
if  a  number  of  trees  sufficient  to  give  good  average  results  are  used.  The 
object  of  the  method  described  in  this  problem  is  to  reduce  the  number  of  cal- 
culations to  a  minimum.  Mlodjianski's  principle  is  first  to  determine  by 
means  of  separate  curves  the  average  dimensions  of  the  trees  at  different  ages, 
and  from  them  to  calculate  the  volume  growth  rather  than  to  calculate  the 
volumes  first  and  then  determine  the  averages.  Graves'  modification  con- 
sists in  arranging  the  averaged  curves  in  graphic  form  on  one  sheet  of  cross- 
section  paper  in  such  a  manner  that  the  dimensions  of  a  tree  of  any  age  may  be 
determined  at  a  glance.  The  principle  underlying  the  method  as  proposed  by 
Graves  is  to  have  the  curves  for  the  diameter  growth  at  each  cross-cut  placed 
on  the  co-ordinate  paper  with  reference  to  the  total  age  of  the  tree  instead  of 
the  number  of  rings  at  the  cross-cut  in  question.  Remember,  that  the  age  at 
the  stump  does  not  represent  the  total  age  of  the  tree,  because  no  rings  are 
represented  in  the  cut  surface  of  the  stump  for  those  years  during  which  the 
tree  grew  to  stump  height.  The  problem,  then,  is  to  show  in  the  diameter 
growth  curve  for  the  stump  how  many  years  in  the  whole  life  of  the  tree  it  took 
to  produce  a  stump  of  a  certain  diameter  and  not  how  many  years  after  the 
tree  had  grown  to  stumj)  height.     In  this  problem  the  curve  for  each  cross-cut 


GRAVES'   MODIFICATION  OF  MLODJIANSKI'S  METHOD       67 

will  then  begin  to  the  right  of  the  original  zero,  at  th(>  intersection  of  the 
co-ordinate  axes,  as  many  units  (years)  as  it  took  the  tree  to  grow  from  the 
ground  to  the  respective  cross-cuts. 

Directions: 

A.  Data  Required. — Complete  stem  analysis  of  trees  cut  into  logs  of  equal 

length  where   possible.     Unless  other  data  are  available   the   three 
selected  trees  of  Data  Series  V.  will  suffice  for  purposes  of  illustration. 

B.  Method. — Plotting  the  values  before  averaging. 

C.  Method  of  Procedure. 

1.  Construct  a  height  growth  table  showing  the  average  time  required 

for  the  trees  to  grow  from  the  ground  to  the  various  cross-cuts. 

2.  Determine  the  average  stump  heights. 

3.  Draw  a  diameter  growth  curve  for  the  stump  just  as  was  done  in 

Problem  26.  Label  it  Stump  Curve  and  indicate  the  average  stump 
height  on  it. 

4.  In  a  similar  manner,  and  with  the  same  values  for  abscissae  and  ordi- 

nates,  draw  a  separate  diameter  growth  curve  for  each  of  the  suc- 
ceeding cross-cuts,  i.e.,  if  the  average  stump  height  is  2  feet  and  the 
logs  are  cut  in  16-foot  lengths,  the  second  curve  will  represent  the 
growth  at  a  point  18  feet  above  the  ground,  the  third  at  a  point 
34  feet  above  the  ground  and  so  on.  Label  each  with  its  average 
distance  above  ground 

5.  Now  transfer  all  the  curves  to  one  sheet  in  such  a  manner  that  the 

growth  at  the  respective  cross-cuts  will  be  shown  on  the  basis  of 
total  age,  i.e.,  let  each  curve  begin  as  many  years  to  the  right  of  the 
intersection  of  the  two  axes  as  it  took  the  tree  to  grow  to  the  height 
of  the  cross-cut  in  question.  Determine  this  point  in  each  case 
from  the  height  growth  table.  Do  not  transfer  the  curves  by 
means  of  pin  pricks,  but  plot  the  average  values. 

6.  Determine  the  average  height  of  the  oldest  trees  from  the  height 

growth  curve.  Indicate  this  average  by  drawing  a  short  perpen- 
dicular through  the  age  axis  at  the  proper  point,  and  label  it  "Aver- 
age Total  Age,"  below  the  axis.  Just  above  the  axis  at  this  point 
write  in  the  average  total  height  and  label. 

7.  These  curves  represent  the  diameter  growth  at  their  respective  dis- 

tances above  ground,  on  the  basis  of  total  age  (the  age  at  the  ground) 
and  not  on  the  basis  of  the  age  at  the  respective  cross-cuts.  The 
points  on  the  age  axis  together  with  the  average  total  age,  the 
average  total  height  and  the  points  where  the  curves  at  different 
heights  cross  the  axis  represent  height  growth.  Hence  this  series 
of  curves  will  give  for  any  age  the  dimensions  of  the  trees,  D.I.B. 
at  various  points  along  the  bole,  and  the  total  heights.  For  points 
at  distances  above  the  ground  that  are  intermediate  between  the 


68  GENERAL  GROWTH  OF  STUDIES 

curves  constructed  interpolate.  A  D.B.H.  growth  curve  mav  also 
be  added  l)y  the  method  of  Problem  28. 

8.  Determine  the  dimensions  of  the  trees — D.I.B.  at  the  stump,  and  at 

the  end  of  each  section  (log)  and  the  total  height — for  even  10-year 
periods  beginning  with  10  years,  and  proceeding  through  to  the  time 
the  trees  were  cut.     Arrange  in  table  form. 

9.  From  the  preceding  table  construct  a  Volume  Growth  Table  showing 

(a)  the  growth  of  the  entire  stem  in  cubic  feet,  and  (6)  the  growth  in 
board  feet  of  the  merchantable  stem,  for  each  10-year  period. 
Consider  6  inches  D.I.B.  for  the  merchantable  top  diameter  limit. 
Use  the  International  Log  Rule,  or  any  other  with  values  down  to 
6  inches  top  diameter  for  determination  of  board  foot  contents. 

PROBLEM  32.     (Office.)     The  Determination  of  Maximum  Growth 

Explanation. — The  object  of  determining  maximum  growth  is  chiefly  for  the 
purpose  of  finding  out  how  fast  all  the  trees  in  an  unthinned  stand  would 
grow  assuming  that  each  could  be  made  to  grow  as  fast  as  the  most  rapidly 
growing  trees,  providing  they  were  given  the  proper  treatment.  Thie 
method  of  procedure  as  given  in  the  accompanying  illustration  would  be 
applicable  to  any  of  the  various  kinds  of  growth  studied  and  may  be  applied 
to  any  of  the  succeeding  growth  exercises.  The  data  for  this  exercise  may 
be  obtained  either  by  analysis  of  a  large  number  of  trees  of  different  sizes,  or 
by  selecting  only  the  maximum  trees  for  analysis.  In  the  latter  case  the 
maximum  growth  would  be  determined  directly  from  these  analyses  by  the 
same  method  of  procedure  as  described  in  Problem  26,  if  collected  by  first 
method  referred  to,  as  described  in  the  illustration  below. 

Illustration. — To  Determine  the  Maximum  Diameter  Growth  at  the  Stump 
in  Even-aged  Stands  by  Constructing  a  Maximum  Diameter  Growth  Curve. 

Directions: 

A.  Data  Required. — Stump  analyses  and  total  ages  of  selected  trees  of  differ- 

ent sizes.     As  the  values  are  plotted  exactly  as  in  Problem  26,  the 
same  sheet  of  cross-section  paper  with  its  plotted  points  may  be  used. 

B.  Method  of  Procednre. 

1.  Using  the  same  sheet  of  cross-section  paper  with  its  plotted  points 

that  was  used  in  Problem  26,  draw  a  smooth  curve  as  an  upper 
boundary  to  the  main  body  of  the  plotted  points,  being  careful  to 
exclude  all  points  that  indicate  abnormally  high  values. 

2.  Read  off  a  table  showing  the  diameters  of  the  maximum  trees  for 

each  even  10  years. 


SECTION    IX.    SAMPLE    PLOT    STUDIES 

Explanation. — Sample  plot  studies  are  useful  for  the  determination  of  the 
contents  of  stands,  for  solving  certain  problems  in  growth,  and  as  a  prelimi- 
nary step  in  the  construction  of  yield  tables.  In  order  that  all  of  these 
different  problems  may  be  worked  out  as  laboratory  exercises  from  the 
same  felled  sample  trees,  and  that  unnecessary  duplication  of  work  may  be 
avoided,  this  section  is  placed  immediately  following  the  section  on  Growth 
Studies. 

The  underlying  principle  in  all  sample  plot  studies  is  to  obtain  the  desired 
information  by  the  measurement  of  a  few  carefully  selected  average  trees  in 
sample  plots  representing  average  conditions,  and  then  to  apply  the  com- 
bined average  results  as  obtained  from  the  sample  plots  to  an  entire  tract. 
It  should  not  be  necessary  to  emphasize  here  that  the  greater  the  number  of 
plots  used  the  greater  will  be  the  accuracy  of  the  results. 

For  a  rough  check  in  practical  work,  or  where  sample  trees  ^an  not  be 
felled  a  standard  volume  table  may  be  used  to  determine  the  volumes  of 
the  sample  trees.     Do  not  do  this  where  great  accuracy  is  required. 

PROBLEM  33.     (Field.)     The  Determination  of  the  Contents  of  a  Stant) 
BY  Means  of  Felled  Sample  Trees. 

ExPLitN  ATiON . — The  accompanying  illustrations  include  three  distinct 
methods.  With  them  as  a  foundation  the  student  should  have  no  difficulty 
in  understanding  the  underlying  principles  of  any  method.  It  is  suggested 
that  this  e.xercise  be  carried  out  in  young,  nearly  even-aged  stands.  They 
will  serve  the  purpose  of  illustration  fully  as  well  as  older  stands,  and,  further, 
will  result  in  a  considerable  saving  of  time  and  unnecessary  manual  labor. 
Each  student  should  have  a  complete  set  of  all  the  data  and  calculations 
obtained  by  the  other  members  of  his  party.  These  should  be  collected 
from  the  other  members  immediately  after  each  problem  has  been  completed. 
In  each  of  the  accompanying  illustrations  arrange  the  data  and  the  results  in 
logical  order  so  that  each  step  will  be  indicated  in  the  proper  place. 

Illustration  I. — The  Mean  Sample  Tree  Method. 

Principle. — The  principle  of  this  method  is  to  base  the  contents  of  the  sample 
plot  on  the  contents  of  one  or  more  trees,  each  of  which  represents  the 
average  of  all  the  trees  within  the  sample  area. 

69 


'0  SAMPLE   PLOT  STUDIES 

DlKLX'TlONS:         • 

A.  Parties. — A  men.     'I'lic organization  of  (he  work  for  each  man  is  loft  to 

the  "Chief  of  I^irty  "  designated  by  the  instructor.  lie  will  be  marked 
on  the  efficiency  with  which  his  party  carries  out  the  work.  Remember 
that  every  man  should  be  kept  busy. 

B.  Equipment  Required. 
1   100-foot  steel  tape. 

1  surveyor's  compass,  or  1  angle  mirror. 

2  pairs  of  tree  calipers. 
1  cross-cut  saw. 

1  hand  axe. 

2  bark  scratchers  (white  carpenter's  chalk  often  answers  the  purpose 

even  better) . 

3  field  notebooks  (one  per  man),  with  blank  Forms  1,  2  A,  and  3  A,  and 

cross-section  paper. 

C.  Method  of  Procedure. 

1.  Determine  the  area  of  the  tract.     In  order  to  save  time  assume  an 

arbitrary  area  of  40  acres. 

2.  Make  a  careful  examination  of  the  entire  tract  for  the  purpose  of 

selecting  a  plot  that  will  represent  average  conditions. 

3.  Carefully  lay  off  a  sample  plot  (i  to  r&  acre  will  do  to  illustrate  the 

problem).     Mark  the  bovmdaries  carefully. 

4.  Cafiper  all  the  trees  in  the  sample  area  at  D.B.H.  to  the  nearest  inch, 

down  to  a  minimum  diameter  of  2  inches.  Mark  each  tree  calipered, 
to  avoid  repetition.  For  convenience  in  recording  the  measurements 
use  a  form  similar  to  that  used  when  cruising  on  the  basis  of  diameters 
only.     (Form  3  A.) 

5.  Arrange  all  data,   including  the  calculated  values,   in  a  convenient 

tabular  form. 

6.  Determine  the  diameter  of  the  average  tree  by  the  formula: 

6ini+52n2+63^i3  4-etc. 
''  =  - N • 

in  which  6  =  the  average  basal  area  of  all  trees  on  the  plot; 

6i,  hi,  etc.  =  basal  areas  of  the  ditTerent  diameters; 

Ml,  n-,,  etc.  =  number  of  trees  of  each  diameter; 
A^  =  total  number  of  trees  on  the  plot. 
Use  table  of  basal  areas  for  getting  the  diameter  values  of  h. 

7.  Cut  three  trees  whose  diameters  fall  within  0.5  of  an  inch  of  the  diam- 

eter of  the  average  tree.  Be  careful  to  select  trees  of  average  height 
and  crown  development.  Number  the  stump  of  each  tree  to  corre- 
spond ivith  the  number  of  the  record  sheet  so  that  both  may  be  used  for 
future  problems.     Record  measurements  on  Form  2  A. 


STAND   BY   MEANS  OF   FELLED   TREES  71 

8.  Determine  the  volume  of  each  in  cubic  feet  bj^  Smahan's  method, 

using  10-foot  sections. 

9.  In  order  to  correct  any  error  resulting  from  a  difference  in  the  diameters 

of  the  sample  trees  and  that  of  the  average  tree  as  calculated  deter- 
mine the  contents  of  the  average  plot  by  the  formula : 

vXB 
^  ~     b    ' 

in  which  l'  =  the  volume  of  the  average  acre; 
/'  =  average  volume  of  test  trees; 
/?=  total  basal  area  of  the  plot; 
6  =  average  basal  area  of  the  test  trees. 

Reduce  to  acre  terms. 
10.  Determine  the  contents  of  the  entire  stand.     (40  acres  assumed.) 

Illustration  II. — The  Arbitrary  Group  Method. 

Principle. — The  principle  of  the  method  is  to  group  all  the  trees  measured  on 
the  plot  into  arbitrary  D.B.H.  classes.  Each  group  is  then  treated  in 
exactly  the  same  manner  as  were  all  the  trees  in  the  Mean  Sample  Tree 
Method.  The  chief  difference  between  this  and  all  other  methods  in 
which  the  trees  are  grouped  is  in  the  manner  of  grouping  and  the  number 
of  test  trees  to  be  cut. 

Directions: 

A.  Parties  ami  Equipment  a.s  in  Illustration  I. 

B.  Method  of  Procedure. 

1.  Use  the  same  area  for  the  tract,  the  same  plot  and  the  same  diameter 

measurements  of  the  standing  trees  as  in  Illustration  I. 

Note. — The  same  plot  is  here  suggested  for  each  illustration  given  in  order  to  give  the 
student  a  thorough  basis  for  comparing  the  different  methods.  Sometimes  the  plots  can  be 
located  in  timber  which  will  be  cut  before  the  completion  of  the  course  in  mensuration.  In 
that  case  all  the  trees  can  be  carefully  measured,  and  the  contents  can  be  computed  accu- 
rately from  the  felled  trees  and  then  compared  with  the  results  obtained  by  the  different 
sample  plot  methods. 

2.  Group  the  diameter  measurements  into  three  or  four  groups,  so  that 

each  group  or  diameter  class  does  not,  so  far  as  possible,  vary  by 
more  than  4  inches. 

3.  Proceed  with  each  group  (diameter  class)  just  exactly  as  was  done  for 

all  the  trees  in  Illustration  I.     Record  sample  tree  measurements  on 
Form  2  A. 

4.  Arrange  all  data  in  tabular  form  similar  to  that  used  in  Illustration  I. 

5.  From  these  measurements  now  determine  the  cubic  foot  contents  of 
the  40-acre  tract. 


72  SAMPLE   PLOT   STUDIES 

Illustration  III. — The  Volume  Curve  Method. 

Principle. — This  method  differs  from  all  others  in  that  no  determination  of 
average  trees  is  necessary.  The  underlying  principle  depends  upon  the 
construction  of  a  volume  curve  based  on  D.B.H.  made  from  a  few  trees 
selected  so  that  the  small,  the  medium  and  the  large  sized  trees  are  repre- 
sented. 

Directions: 

A.  Parlies  and  Equipment  as  in  Illustrations  I  and  II . 

B.  Method  of  Procedure. 

1.  Use  the  same  area  and  the  same  sample  plot  with  its  tree  measurements 

as  in  Illustrations  I  and  II. 

2.  Select  6  sample  trees  without  reference  to  any  particular  diameter  but 

apportioning  them  so  that  the  large  and  the  small  trees  will  be 
represented,  and  so  that  in  a  measure  the  diameters  for  which  the 
largest  number  of  trees  have  been  recorded  will  be  given  the  largest 
number  of  sample  trees. 

3.  Fell  the  sample  trees,  and  determine  their  total  cubic  foot  contents, 

without  bark,  by  means  of  ten-foot  sections. 

4.  On  a  sheet  of  cross-section  paper  now  plot  the  volumes  of  the  sample 

trees  on  their  diameters  (D.B.H.) .  Draw  a  smooth  curve,  and 
read  off  a  table  of  volumes  for  diameters  in  whole  inches. 

5.  Apply  the  volume  table  to  the  measurements  of  the  trees  on  the  plot 

to  determine  the  contents  of  the  whole  plot  and  from  the  latter  the 
contents  of  the  tract. 

C.  Discussion. 

1.  Comment  on  the  three  methods  giving  your  views  on  the  advantages 

and  disadvantages  of  each  with  reasons. 

2.  Outline   methods   of  procedure   for   the    Urich   and   for   the   Draudt 

methods. 

3.  What  per  cent  of  a  tract  should  be  measured  to  insure  a  good  estimate? 

PROBLEM    34.     (Field.)     The    Determination   of   the   Rale   of  Growth   in 
Even-aged  Stands  by  the  Analysis  of  Felled  Sample  Trees. 

Explanation. — This  exercise  endeavors  to  illustrate  in  a  practical  manner 
the  chief  problems  in  growth  in  even-aged  stands  that  may  be  solved  by 
means  of  felled  sample  trees.  As  the  details  of  the  method  of  procedure 
have  been  illustrated  in  connection  with  previous  problems  the  student  should 
be  able  to  carry  out  the  work  of  the  accompanying  illustration  from  very 
general  directions,  and  the  directions  in  the  Method  of  Procedure  have  been 
so  made.     The  scheme  will  serve,  in  addition  to  illustrating  the  problems 


RATE   OF   GROWTH   IX   EVEN-AGED   8TAXDS  73 

involved,  as  a  thorough  review  of  the  prorediire  in  growth  stucUes.  Refer- 
ences are  made  to  previous  problems,  but  the  student  will  gain  the  greatest 
benefit  from  this  exercise  if  he  does  not  make  use  of  them  until  he  has  found 
by  actual  Irial  that  he  cannot  work  out  the  problems  without  using  the 
references, 

Directions: 

A.  Parties. — 3  mer. 

B.  Equipment. — After  reading  over  the  exercise  the  student  should  deter- 

mine what  equipment  is  required.  (See  Problems  6  and  7.)  Ask  the 
instructor  if  yo\i  are  right  before  starting  for  the  field.  The  chief  of 
party  will  be  held  responsible. 

C.  Method  of  Procedure. 

1.  Use  the  original  data  and  the  felled  sample  trees  obtained  in  the 

Mean  Sample  Tree  method  of  Problem  33. 

2.  Make  a  complete  stem  analysis  of  the  felled  sample  trees.     (Use  regular 

analysis  sheet  for  recording  measurements.     Forms  2,  A  and  B.) 

3.  Work  out  the  following  problems.     Arrange  all  work  in  logical  order: 
(a)  Construct  a  table  of  diameter  growth  at  the  stump.     (See  Problem 

26.) 
(6)   Construct  a  height  growth  table  on  total  age.     (See  Problem  29.) 
(c)   Construct  a  cubic  foot  volume  growth  table  in  10-year  periods. 

Use    Graves'    Modification    of    Mlodjianski's    Method.     (See 

Problem  31.) 
{d)  From  (r)  determine  the  volume  growth  per  acre  in  cubic  feet. 

D.  Discussion. 

1.  Under  what  conditions  would  the  method  of  this  problem  give  satis- 

factory results  concerning  growth?  When  applied  to  mature  stands, 
of  which  trees  onhj  does  it  show  the  growth  throughout  the  entire 
life  of  the  stand? 

2.  Which  of  the  following  methods  would  give  the  most  satisfactory 

results  for  a  growth  study:  Mean  Sample  Tree,  Arbitrary  Group, 
Draudt,  or  Urich?     Why? 

3.  How  many  plots  would  be  considered  sufficient  for  a  reliable  study  in 

any  one  type?  How  large  would  you  say,  judging  from  your 
studies  involving  the  use  of  plots,  should  plots  ordinarily  be  to 
insure  getting  average  conditions? 

4.  How  would  you  modify  the  method  of  procedure  if  this  problem  were 

to  be  carried  out  in  a  mixed  stand? 


74  SAMPLE   PLOl^   STUDIES 

PROBLEM  35.  (Field  and  OHicc.)  Tmo  J^ETioiiiMiNyVTioN  of  (Iuowth  in 
Even-aged  Stands  by  the  Measurement  ok  Standing  'J' ires. 
Explanation. — In  the  method  of  the  last  problem  (No.  33)  it  will  be  remem- 
bered that  good  results  can  be  obtained  only  when  worked  up  in  mature 
stands,  and  that  the  results  will  then  show  the  rate  of  growth  of  only  those 
trees  which  reach  maturity.  The  method  of  this  exercise  will  show  the 
average  rate  of  growth  of  all  trees  throughout  the  life  of  the  stand.  As  it  is 
only  a  comparatively  small  step  from  this  exercise  to  the  fundamental  prob- 
lems involved  in  the  construction  of  yield  tables  showing  the  average  total 
stand  per  acre  at  any  period  in  the  life  of  the  stand,  the  exercise  is  here  out- 
lined so  as  to  cover  the  necessary  work  for  these,  namely  to  select  the  plots 
located  in  different  site  qualities  and  to  calculate  values  in  terms  per  acre. 

This  problem  requires  second  growth  even-aged  stands  of  diiferent  ages. 
In  order  that  a  sufficient  number  of  plots  may  ])e  measured  to  insure  CTiough 
to  illustrate  the  exercise  the  instructor  should  at  the  outset  arrange  the  work 
of  each  party  in  such  manner  that  as  large  a  range  of  ages  will  be  olitained  as 
the  conditions  of  the  locality  and  the  sis^e  of  the  class  will  warrant.  The 
students  should  now  be  able  to  carry  out  this  work  without  much  super- 
vision by  the  instructor,  and  the  different  parties  can  be  scattered  over  a 
wide  territory. 
Directions: 

Part  I.— l^ield  Work 

A.  Parties. — 3  men  in  each. 

B.  Equipment. — Determine    what  instruments   and    other  equipment    are 

necessary  for  each  party,  and  have  the  instructor  check  your  list  before 
starting  for  the  field.     The  chief  of  party  will  be  held  responsible. 

C.  Method  of  Procedure. 

1.  Carefully  lay  off  sample  plots  of  re"?  a-cre  in  stands  of  different  ages. 

If  good  average  conditions  cannot  be  found  in  ^-acre  plots,  larger 
plots  should  be  used.  In  order  that  these  same  data  may  be  used 
in  connection  with  the  work  in  yield  tables,  some  effort  should  be 
made  to  secure  them  from  different  site  qualities. 

2.  Measure  all  trees  at  D.B.H.  and  record  as  in  cruising. 

3.  Number    and  describe  the   locality  of  each  plot  on  the  tally  sheet. 

Use  U.  S.  land  subdivisions  where  possible. 

4.  Determine  the  following  information  in  the  field  with  reference  to 

each  plot,  using  the  Mean  Sample  Tree  Method  for  determining  any 

points  requiring  felled  sample  trees, 
(a)  The  number  of  trees  per  acre. 
{h)  The  diameter  of  the  average  tree, 
(c)   The  volume  of  the  average  tree. 
{d)  The  average  height.     (Measure  6  to  10  representative  trees  of 

the  average  diameter  with  the  hypsometer  and  average.) 
ie)   The  average  age. 


GROWTH  IN  EVEN-AGED  STANDS  75 

Part  II.— Office  Work 

Note.— In  order  that  enough  data  for  the  construction  of  a  table  may  be  at  hand  the 
field  work  of  the  entire  class  should  be  collected  for  the  use  of  each  student.  (For  schools 
8o  situated  that  it  is  impracticable  to  collect  appropriate  data,  Data  Series  VI  has  been 
included  in  the  Appendix.) 

A.  Construct  a  table  giving  the  following  information  in  10-year  periods: 

(a)  The  average  number  of  trees  per  acre; 

ib)  The  dianieter  of  the  average  tree; 

(c)  The  average  diameter; 

(d)  The  average  total  basal  area  in  acre  terms; 

(e)  The  average  height; 

(/)    The  average  volume  in  cubic  feet  in  acre  terms. 
Note. — All  average  values  should  be  evened  off  by  curves. 

B.  Arrange  all  data,  curves  and  other  work  in  logical  order. 

C.  Discussion. 

1.  Outline  the  measurements  and  office  work  required  as  if  the  object 

were  to  show  only  the  growth  at  D.B.H.  in  10-year  periods. 

2.  Compare  this  method  with  that  of  Problem  33  with  reference  to  the 

conditions  under  which  each  would  be  applicable. 

3.  Could  this  method  be  modified  for  the  determination  of  growth  in 

uneven-aged  stands?  If  so,  show  how  you  would  modify  it.  If 
not,  why  not?  Consider  in  your  reply  the  difference  in  the  character 
of  the  stands,  and  in  the  silvicultural  conditions  of  growth,  and  the 
method  of  studying  growth  in  uneven-aged  stands.  (See  Problem 
27.) 

4.  Would  the  method  be  applicable  to  mixed  stands?     Show  how,  or, 

if  not  applicable,  wh}^  not? 

5.  Which  would  you  consider  the  more  accurate  for  the  determination 

of  the  average  age,  the  average  age  of  the  sample  trees  or  the  aver- 
age age  of  the  dominant  trees?    Why? 


SECTION  X— STUDIES  IN  GROWTH  PER  CENT 

Explanation. — Growth  per  cent  is  chiefly'  useful  in  the  prediction  of  volume 
growth  for  short  periods,  and  is  a  method  used  in  connection  with  the  prepa- 
ration of  working  plans  for  even-aged  stands,  and  in  the  determination  of 
the  final  volume  to  be  cut.  Equipment  required  for  field  work  is  not  listed 
with  the  exercises  of  this  section.  The  chief  of  party  will  in  each  case  be 
held  responsible  for  checking  out  the  necessary  equipment. 

PROBLEM    36.     (Field.)     The    Determination    of    Futuhe    Volume    by 
Means  of  Growth  Per  Cent  Calculated  Frotn  Felled  Sample  Trees. 

Explanation. — This  exercise  aims  to  illustrate  three  of  the  fundamental 
methods.  For  purposes  of  comparison  it  is  suggested  that  all  of  them  be 
carried  out  on  the  same  sample  plot. 

IL1.USTRATION. — To  Determine  What  the  Volume  in  Cubic  Feet  of  a  40-acre 
Tract  (area  assumed)  Will  Be  10  Years  Hence. 
Method  1. — By  comparing  the  Average  Volume  Growth  for  the  past  ten 
years  as  interest  to  the  Volume  10  years  ago  as  Principle. 

Directions: 

A.  Formula. 

V-v 

:v  =  p:100, 

n 

V-v 

p  = xioo 

vn 
where  p  =  growth  per  cent; 
V  =  present  volume ; 
«;  =  volume  10  years  ago; 
n  =  10  years. 

B.  Parties. — 3  men  in  each. 

C.  Method  of  Procedure. 

1.  Select  and  carefully  lay  out  an  average  plot  of  j  acre. 

2.  Proceeding  as  in  the  Mean  Sample  Tree  Method,  determine  the  volume 

of  the  plot  and  the  average  tree. 

3.  Select  and  fell  three  average  trees  for  measurement. 

76 


FUTURE  VOLUME   BY   MEANS   OF   GROWTH  77 

4.  Determine  the  present  full-stem  volume  (inside  bark)  and  the  volume 

10  years  ago,  of  each  bj^  means  of  10-foot  sections,  and  average. 

5.  Determine  the  growth  per  cent  by  substituting  in  the  formula  th.e 

values  obtained  in  4. 

6.  Calculate  from  the  growth  per  cent  what  the  volume  of  the  tract 

(assume  40  acres)  will  be  10  years  hence. 
Method  2. — By  Comparing  the  Average  Volume  Growth  for  the  past   10 
years  as  interest  to  the  Average  of  the  Present  Volume  and  the  Volume 
10  years  ago  as  Principle. 

DiRECTION.S: 

A.  Formula. 

V-v     V+v 
n  2 

V-v     200 

V-\-v      n 

The  symbols  are  the  same  as  in  Method  1.     This  is  considered  the  most 
satisfactory  formula  for  all  general  purposes. 

B.  Method  of  Procedure. 

1.  Proceed  as  in  Method  1  using  the  same  felled  sample  trees. 

Method  3. — By  Comparing  the  Average  Volume  Growth  for  the  past   10 
3^ears  as  interest  to  the  Volume  one  year  ago  as  principle. 

Directions: 

A.  Formula. 

n        \  n    I 

V-v 

V  = X 100. 

^     F(n-1)+^' 

B.  Method  of  Procedure. — Proceed  as  in  1  and  2,  using  the  same  felled  sample 

trees. 

C.  Di'iC'i'ifiion. 

1.  Present  the  mathematical  derivation  of  each  of  the  formula)  used. 

2.  Arrange  the  results  of  the  three  methods  in  a  comparative  series. 

Give  your  opinion  of  their  relative  values. 

3.  Which  of  the  above  methods  are  applicable  to  mature,  and  which  to 

young  stands? 

4.  Outline  a  method  of  ])r()cedur('  for  use  in  mixed  stands. 

5.  Are  any  of  the  above  methods  applicable  to  uneven-aged  stands? 

If  not,  why  not? 


100, 


78  STUDIES   IN   GROWTH   PER  CENT 

PROBLEM  37.  (Field.)  The  Determination  of  Future  Volume  in 
Immature  Even-aged  Stands  by  Means  of  Growth  Per  Cent  Calcu- 
lated FROM  Standing  Trees. 

Illustration. — To  determine  what  the  volume  of  a  stand  will  be  ten  years 
hence  by  means  of  Pressler's  formula  for  immature  trees. 

Explanation. — In  this  formula  Presslcr  starts  with  the  factors  of  volume, 

■kD'^HF 

V  = as  a  basis  and  eliminates  F,  the  form  factor,  by  assuming  that 

trees  will  not  materially  change  in  form  in  ten  years,  and  by  further  assuming 
that  the  change  in  height  is  proportional  to  the  change  in  diameter  he  elimi- 
nates the  height  factor,  H,  by  finding  its  value  in  terms  of  the  diameter  thus 
evolving  the  formula  as  given  below  for  immature  trees.  For  mature 
trees  he  evolves  the  formula, 

D2-d2     200 

assuming  that  there  is  practically  no  change  in  either  height  or  form  factor. 

Directions: 

A.  Formula. 

D^-d^     200 

D^+d^      n 
where  p  =  growth  per  cent; 

D  =  D.B.H.  of  present  tree; 

d  =  D.B.H.  of  tree  10  years  ago; 

n  =  10  years. 

B.  Method  of  Procedure. 

1.  Use  the  same  plot  used  in  the  preceding  problem. 

2.  Find  3  standing  trees  of  the  requisite  diameter,  either  on  this  plot  or 

adjacent  to  it. 

3.  With  calipers  find  the  average  present  diameter  of  each  tree  by  means 

of  two  measurements  at  right  angles  to  each  other. 

4.  With  the  increment  borer,  by  means  of  two  borings  at  right  angles  to 

each  other  on  each  tree,  find  the  average  diameter  ten  years  ago. 

5.  Substitute  the  averaged  values  for  D  and  d  of  the  three  trees  in  the 

formula  for  growth  per  cent. 

6.  Calculate  what  the  volume  of  the  tract  (assume  40  acres)  will  be 

10  years  hence. 

C  References. — Numbers  06  and  S2. 

D.  Discussion. 

1.  Show  by  means  of  the  mathematical  derivation  of  Pressler's  formula 
how  he  justifies  the  uso  of  this  formula  for  immature  stands. 


FIXTURE   VOLUME   IX   MATURE   STANDS  79 

2.  Compare  the  results  of  this  exercise  with  tliose  derived  by  the  three 

different  methods  of  the  previous  exercise,  and  conmient  on  the 
efficiency  of  Pressler's  formula. 

3.  What  is  Pressler's  formula  for  mature  or  nearly  mature  stands? 

PROBLEM  38.     (Field.)     The  Prediction  of  Future  Volume  in  Mature 
Stands  BY  Means  of  Growth  Per  Cent. 

Explanation. — Schneider's  formula  is  applicable  only  to  mature  trees.  It 
has  been  found  to  be  one  of  the  most  reliable  and  easily  used  formulae. 

Illustration. — To  determine  what  the  volume  of  a  stand  will  be  10  years 
hence  by  means  of  Schneider's  formula. 

Explanation. — Schneider's  formula  uses  the  periodic  annual  growth  as 
determined  by  the  last  inch  radius  as  interest  and  the  average  of  the  volume 
one  year  ago  and  one  year  hence  as  principle.  He  assumes  there  will  be  no 
change  in  height  or  form  factor. 

DiRECTION.s: 

A.  Formula. 

400 
nD 
where  j)  =  growth  per  cent ; 

D  =  present  D.B.H.  (outside  bark) ; 

n  =  number  of  rings  in  the  last  inch  radius. 

B.  Method  of  Procedure. 

1.  Lay  off  a  sample  area  of  ^  acre  in  an  old  stand  of  timber.     (If  the 

trees  are  very  large  or  scattered  use  1  acre.) 

2.  Determine  the  average  tree  by  means  of  the   Mean  Sample  Tree 

Method. 

3.  Make  the  necessary  measurements  on  three  trees.     Average  and  apply 

in  the  formula  for  growi:h  per  cent. 

4.  By  means  of  the  growth  per  cent  calculate  the  volume  of  the  tract 

(40  acres)  10  years  hence. 

C.  Discussion. 

1.  Show  step  by  step  how  your  results  were  derived. 

2.  Show  by  means  of  the  mathematical  derivation  of  Schneider's  formula 

why  it  is  not  applicable  to  immature  trees. 


SECTION  XL— YIELD  TABLE  STUDIES 

Explanation. — Yield  tables  are  tabular  statements  which  show  the  average 
stand  of  timber  per  acre.  As  in  volume  and  growth  studies  separate  tables 
are  made  for  stands  growing  under  different  conditions  or  having  distinct 
characters.  »They  are  made  both  for  even-aged  stands  and  for  uneven- 
aged  stands.  Two  forms  are  recognized  for  the  even-aged  stands :  1.  The 
Normal  Yield  Table,  showing  the  stand  per  acre  of  normal  or  fully  stocked 
stands,  and  2.  The  Empirical  Yield  Table,  showing  the  average  stand  in 
any  locality  irrespective  of  stocking.  By  a  fully  stocked  stand  is  meant  one 
with  the  average  maximum  yield  obtainable  under  the  existing  conditions. 

The  construction  of  yield  tables  for  even-aged  stands  does  not  present 
any  great  difficulties.  Yield  tables  for  many-aged  stands,  however,  offer  a 
number  of  serious  difficulties.  Up  to  the  present  time  there  has  been  no 
general  method  devised  for  constructing  these  that  is  wholly  satisfactory. 
For  this  reason  problems  for  many-aged  stands  have  been  omitted,  but  a  list 
of  references  to  the  various  methods  is  included  at  the  end  of  this  section. 
In  dealing  with  yield  tables  the  student  should  remember  that  he  is  dealing 
with  values  per  acre. 

PROBLEM  39.     (Office.)     The  Construction  of  Yield  Tables  for  Even- 
aged  Stands. 

Explanation. — In  the  foregoing  problems  the  student  has  had  practice  in 
nearly  all  the  steps  necessary  for  the  construction  of  the  different  kinds  of 
yield  tables  for  even-aged  stands.  The  Method  of  Procedure  in  Problem  35 
covers  practically  all  of  the  points  necessary  for  the  collection  of  field  data. 
In  fact  in  that  exercise  the  student  has  virtually  constructed  an  Emjyirical 
Yield  Table.  All  that  is  now  necessary  to  further  illustrate  the  work  is  to 
take  up  the  special  problems  that  arise  in  connection  with  the  construction 
of  Normal  Yield  Tables. 

Illustration. — To  Construct  a  Normal  Yield  Table  for  IJuthinned  Pure 
Stands. 

Directions: 

A.  Data  Required. — The  measurement  of  permanent  sample  plots  would  of 

course  give  the  best  results.     However,  when  time  is  an  important 

consideration  these  are  out  of  the  question,  since  it  would  take  years  to 

collect  the  necessary  data  by  this  means.     To  overcome  the  difficulty 

80 


YIELD   TABLES   FOR   EVEN-AGED   STANDS  81 

of  the  time  element  we  measure  a  large  number  of  sample  plots  in 
even-aged  stands  from  youth  to  maturity,  in  different  site  qualities, 
and  as  fully  stocked  as  possible.  Use  data  collected  (or  used)  in 
Problem  35. 

B.  Method  of  Procedure. 

1.  Group  the  plots  into  3  site  qualities. 
Method  I.— Bauer's  Method  of  Bands. 

(a)  Plot  the  volumes  (cubic  feet)  in  acre  terms  on  age.  In  each  case 
be  sure  to  place  the  number  of  the  plot  with  the  plotted  points. 
(The  data  of  Series  IV  are  arranged  according  to  site  quahties.) 

(6)  Enclose  the  plotted  points  between  2  regular  curved  lines. 
Divide  the  space  between  them  into  3  equal  bands  by  first 
indicating  the  proportional  distances  on  the  vertical  lines 
from  the  abscissa  axis  at  each  10-  or  20-year  point  and  then 
join  the  indicating  marks  by  regular  curves. 

(c)  Include  all  plots  in  the  highest  band  in  Site  Quality  I,  those 
in  the  middle  in  Site  Quality  II,  and  those  in  the  lowest  in 
Site  Quality  III. 

Method  II.— The  Site  Factor  Method. 

(a)  Determine  the  site  factor  for  each  plot  by  means  of  the  following 
formula : 

a 

in  which  F  =  the  site  factor; 

/i  =  the   height   of  the  average  tree,   which  is  to  be 
determined  from  a  height-diameter  curve.     The 
height  of  the  average  tree  is  to    be  taken  as  the 
height  shown  for  the  tree  of  average   diameter; 
B  =  basal  area  in  square  feet  per  acre; 
a=the  average  age  of  the  stand. 
(6)   Divide  all  the  site  factors  into  3  groups    of  equal  numerical 
range  in  volume.     All  plots  whose  site   factor  falls  within  the 
range  of  the  highest  group  ^nW  belong  to  Site    Quality  I, 
those  of  the  middle  group  into  Quality  II,    and  those  of  the 
lowest  into  Quality  III. 
(c)    Determine  the  basal  areas  and  plot. 

id)  Arrange  the  results  obtained  by  the  two  methods  in  a  compara- 
tive table. 

2.  Determine  the  normality  of  stocking  by  Bauer's  Method  as  follows: 
(a)  Draw  an  average  curve  and  exclude  from  the  investigation  all 

I)lots  whose  volumes  vary  by  more  than  7.5  per  cent  from  the 
average.     These  are  either  abnormally  stocked  or  understocked. 


82  YIELD   TABLE   STUDIES 

(b)  Normality  ran  also  l)o  determined,  and  that  often  more  rapidly  by 
comparing  the  basal  areas  of  all  plots  of  the  same  age  and  site 
cjuality  without  curves  as  follows: 

1.  Determine   the   average   total   basal  areas  of  plots   of   same 

average  age. 

2.  Plots  whose  areas  do  not  fall  within  7.5  per  cent  of  this  average 

are  discarded. 

3.  Average  the  plotted  points  of  each  site    quality  separately,    even 

off  with  a  regular  curve,  read  ofT  the  average  volume  per  acre  in 
10-year  periods,  and  arrange  in  table  form. 

4.  In  addition  to  the  yield  the  Normal  Yield  Table  should  also  include 

the  following  information  for  each  10-year  age  period : 

(a)  The  average  height; 

(6)   The  average  diameter  (D.B.H.); 

(c)  The  number  of  trees  per  acre; 

(d)  The  total  basal  area  in  acre  terms; 

(e)  Sometimes  also  the  form  factor  and  the  growth  per  cent. 

All  of  the  above  are  determined  just  as  they  were  in  Prob- 
lem 34,  except  that  stands  not  normally  stocked  are  not  in- 
cluded and  all  calculations  are  made  separately  for  each  site 
quality. 

C.  References. — Numbers  71,  74  and  86. 

D.  Discussion. 

1.  Name  in  the  order  of  procedure  all  the  important  steps  necessary  in 

the  collection  of  data  for  the  construction  of  a  Normal  Yield  table. 

2.  What  other  factors  beside  volume  may  be  used  to  determine  normality 

of  stocking?     Under  what  circumstance  would  it  be  more  advan- 
tageous to  use  a  different  factor? 

3.  What  factor  beside  volume  may  be  used  to  determine  site  quality  by 

Bauer's  Method  of  Bands? 

4.  What  would  be  the  chief  difference  in  the  collection  of  data  for  Normal 

and  Empirical  Yield  Tables? 

5.  Outline  briefly  the  main  steps  in  the  method  of  procedure  for  collect- 

ing data  for  a  yield  table  thinned  for  the  first  time  in  late  life. 

6.  Outline  briefly  a  method  of  procedure  for  a  yield  table  for  mixed 

stands,  assuming  that  we  have  an  even-aged  stand  of  Douglas  Fir 
with  an  under-story  of  hemlock. 

PROBLEM  40.     (Field.)     Method  of  Using  Yield  Tables  in  the  Field. 

Explanation. — Yield  tables  are  used  to  show  the  future  returns  from  planta- 
tions and  immature  stands,  for  estimating,  for  the  determination  of  site 
quality,  and,  with  reference  to  working  i)lans,  the  growing  stock,  the  normal 
yield  and  the  rotation.     That  the  students  may  work  this  exercise  out  prac- 


METHOD  OF  USING  YIELD   TABLES  IN   THE   FIELD        83 

tically,  it  will  be  necessary  to  i)lace  in  their  hands  a  yield  table  applicable  to 
the  section  of  the  country  in  which  they  are  working.  A  yield  table  for 
Second  Growth  Douglas  Fir  will  be  found  in  the  Appendix.  Others  can 
sometimes  be  obtained  in  Forest  Service  publications  dealing  with  the 
particular  region  in  question,  or  they  may  in  some  cases  be  obtainable  from 
the  Forester  at  Washington,  D.  C.  The  illustrations  given  below  are  out- 
lined with  reference  to  Normal  Yield  Tables.  If  these  are  not  available 
Empirical  Tables  will  do,  but  in  that  case  provision  should  be  made  in  the 
directions  for  the  discrepancy  that  will  arise  in  connection  with  the  question 
of  normality  of  stocking. 

Choose  for  the  purpose  of  illustrating  this  exercise  young,   even-aged 
stands,  preferably  under  50  years  old,  and  as  fully  stocked  as  possible. 
Illustration  I. — To  Estimate  the  Contents  of  a  Stand. 

A.  Parties. — 3  men  in  each. 

B.  Equipment. — To  be  determined  by  chief  of  party. 

C.  Method  of  Procedure. — Lay  out  a  representative  plot  of  ^    acre   in  the 

tract  to  which  the  table  is  to  be  applied  and  by  means  of  the  Mean 
Sample  Tree  IMethod  determine  the  following: 

1.  The  average  age  of  the  stand  as  the  age  index.     When  the  age  is  not 

an  even  multiple  of  10,  all  calculations  will  need  to  be  reduced  by 
proportion  to  the  nearest  10-year  period  in  the  table. 

2.  The  average  height  *  of  the  stand  as  an  index  to  the  site  quality. 

3.  The  total  basal  area  (in  acre  terms)  as  in  index  to  the  normality  of 

stocking.     This  should  be  stated  in  terms  of  the  per  cent  of  the 
total  basal  area  indicated  in  the  table. 

4.  The  ijield.     Reduce  the  yield  indicated  in  the  table  by  the  per  cent 

of  stocking. 
Illustration  II. — To  determine  what  the  Volume  of  the  Stand  will  be  when 
it  is  100  years  old. 

A.  Method  of  Procedure. — With  the  information  obtained  in  Illustration  I 

it  is  now  only  necessary  to  refer  to  the  table  to  obtain  the  future  yield. 
The  yield  indicated  for  the  100-year-old  stand  should  be  reduced  by 
the  per  cent  of  stocking. 

B.  References. — Number  68. 

C.  Discussion. — In  the  two  illustrations  given  above  no  use  was  made  of: 

(a)  The  number  of  trees  i)er  acre;  (b)  The  average  diameter  at  the 
different  ages;  (c)  The  form  factor.  What  is  the  object  of  including 
these  in  a  yield  table? 

Uneven-aged  Stands 

The  following  references  may  be  helpful  in  understanding  the  question 
of  yield  tables  for  uneven-aged  stands:  Numbers  69,  70,  75,  77,  78  and  79. 

*  If  the  site  factor  has  been  established  for  the  region  it  may  be  used. 


APPENDIX 


A  DIAGRAM  FOR  THE  CORRELATION  OF  METHODS  IN 
FOREST  MENSURATION 

(Explanation) 

The  accompanying  diagram  will  show  with  reference  to  the  character  of  the 
stand  (forest  description)  the  data  required  and  the  method  of  computation  for 
practically  all  problems  in  growth  studies.  It  also  serves  to  correlate  and  illus- 
trate the  relationship  between  the  various  different  individual  problems. 

To  use  the  diagram  begin  at  the  center  and  follow  an  imaginary  radius  line 
straight  from  the  center  through  the  sections  that  will  indicate  the  character  and 
previous  treatment  of  the  stand  (forest  descrii)tion)  to  Data  Required;  read  the 
data  indicated  opposite  diameter,  height,  volume  or  yield  as  required;  continue 
the  same  radius  into  the  circle  marked  Computations  and  read  as  indicated  for 
the  type  of  study. 

E.xample*  Desired  a  volume  growth  tal)lc  for  Even-aged,  Pure  Stands, 
Regularly  Thinned: 

Begin  at  center — Follow  a  radius  that  cuts  the  even-aged  sector,  the  pure- 
stand  sector,  and  the  regularly-thinned  sector  to  "data  required."  In  this  circle 
we  have  indicated  opposite  "Vol."  the  data  required  for  this  study.  Continue 
this  same  radius  to  the  circle  marked  "Computations,"  the  methods  of  working 
up  the  data,  as  indicated  opposite  "Vol." 


BIBLIOGRAPHY 

The  Following  lu /."rencefi  arc  Confined  Entirely  to  American  Works  and  Periodicals 

PRELIMINARY   MEASUREMENTS 

1.  Biltmore  Pachymeter.      Ralph  G.  Burton,  Forestry  Quarterly,  Vol.  IV,  No.  1,  p.  9. 

2.  Biltmore  Stick.      A.  G.  Jackson,  Forestry  Quarterly,  Vol.  IX,  No.  3,  p.  406. 

3.  Notes  on   the  Biltmore  Stick.      Donald   Bruce,   Proceedings  of   the  Society  of  American 

Fcfresters,  Vol.  IX,  No.  1,  p.  46. 

4.  A  New  Ilypsometer.      H.  D.  Tieman,  Forestry  Quarterly,  Vol.  II,  No.  3,  p.  145. 

5.  Relative  Accuracy  of  Calipers  and  Diameter  Tape.      N.   VV.  Scherer,   Proceedings  of«the 

Society  of  American  Foresters,  Vol.  IX,  No.  1,  p.  102. 
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Quarterly,  Vol.  XII,  No.  2,  p.  141. 

84 


DIAGRAAI— CORRELATION  OF  METHODS  IN  GROWTH  STUDIES 


A  Diagram  for  the  Correlation  of  Methods  in  Growth  Studies 


85 


86  APPENDIX 

7.  Difficviltics  ami   Errors  in   Stem   Analysis.      A.    S.    Williaiiis.   Forestry  Quarterly,   Vol.    I, 

No.  1,  p.  12. 

8.  New  Aspects  Regarding  Use  of  the  Forest  Service  Standard  Ilypsonieter.      Herman  Krauck, 

Journal  of  Forestry,    Vol.  XVI,  No.  7,  p.  772. 

9.  Method  of  Taking  Impressions  of  Year  Rings  in  Conifers.      L.  S.  Higgs,  Forestry  Quarterly, 

Vol.  X,  No.  1,  p.  1. 

10.  A  New  Timber  Scale.     Judson  F.  Clark,  Forestry  Quarterly,  Vol.  XI,  No.  4,  p.  467. 

11.  Comparative  Test  of  the  Klaussner  and  Forest  Service  Standard  Hypsometers.      D.   K. 

Noyes,  Proceedings  of  the  Society  of  American  Foresters,  Vol.  XI,  No.  4,  p.  417. 

12.  A  Practical  Xylometer.     J.  S.  lUick,  Journal  of  Forestry,  Vol.  XV,  No.  7,  p.  859. 

13.  Mensuration  in  France.      Donald  Bruce,  Journal  of  Forestry,  Vol.  XVII,  No.  G,  p.  G86. 

14.  Determination  of  the   Middle   Diameter  of  a  Standing  Tree.      P.   d'Aboville,  Journal  of 

Forestry,  Vol.  XVII,  No.  7,  p.  802. 

15.  English  Units  for  Measuring  Lumber.     Trotman,  West  Coast  Lumberman,  February  1, 

1915,  p.  21. 

LOG  RULES 

16.  Comparison  of  the  Maine  and  Blodgett  Rules.     Irving  G.  Stetson,  Forestry  Quarterly, 

Vol.  VIII,  No.  4,  p.  427. 

17.  The  Measurement  of  Saw  Logs.      A.  L.  Daniels,  Forestry  Quarterly,  Vol.  Ill,  No.  4,  p.  339. 

18.  The  Measurement  of  Saw  Logs.     Judson  F.  Clark,  Forestry  Quarterly,  Vol.  IV,  No.  2,  p.  79. 

19.  Woodman's  Handbook,  Bulletin  36,  U.  S.  Forest  Service,  Washington,  D.  C. 

20.  Mill  Scale  Studies.      Louis  Margolin,  Forestry  Quarterly,  Vol.  IV,  No.  1,  p.  5. 

21.  Extending  a  Log  Rule.      Edward  A.  BranitT,  Forestry  Quarterly,  Vol.  VI,  No.  1,  p.  47. 

22.  Recent  Log  Rules.     H.  S.  Graves,  Forestry  Quarterly,  Vol.  VII,  No.  2,  p.  144. 

23.  Comparison  of  the  Doyle  and  Scribner  Rules  with  Actual  Mill  Cut  for  Second  Growth 

White  Pine  in  Pennsylvania.      N.  R.  McNaughton,  Forestry  Quarterly,  Vol.  XII,  No.  1, 
p.  27. 

24.  Comparative  Study  of  Scribner  and   Universal   Rules.     J.   Bentley,   Forestry   Quarterly, 

Vol.  XII,  No.  3,  p.  390. 

25.  Log  Scale  in  Theory  and  Practice.     H.  D.  Tieman,  Proceedings  of  the  Society  of  American 

Foresters,  Vol.  V,  No.  1,  p.  18. 

26.  Standardization  of  Log  Measures.     E.  A.  Ziegler,  Proceedings  of  the  Society  of  American 

Foresters,  Vol.  IV,  No.  2,  p.  172. 

27.  Log  Rules,  their  Limitations  and  Suggestions  for  Correction.     H.  E,  McKenzie,  Bulletin  5, 

California  State  Board  of  Forestry. 

PRELIMINARY  CALCULATIONS 

28.  New  Method  of  Measuring  Volume  of  Conifers  (Schiffel  Method).     B.  E.  Fernow,  Forestry 

Quarterly,  Vol.  V,  No.  1,  p.  29. 

29.  Form  of  Bole  of  the  Balsam  Fir.     Judson  F.  Clark,  Forestry  Quarterly,  Vol.  I,  No.  2,  p.  56. 

30.  Alinement  Charts  in  Forest  Mensuration.      Donald  Bruce,  Journal  of  Forestry,  Vol.  XVII, 

No.  7,  p.  773. 

THE  CONSTRUCTION  OF  VOLUME  TABLES 

31.  Volume  Tables  and  the  Bases  upon  Which  They  May  Be  Built.      Judson  F.  Clark,  Forestry 

Quarterly,  Vol.  I,  No.  1,  p.  6. 

32.  Canadian  Volume  Tables.      Ellwood  Wilson,  Forestry  Quarterly,  Vol.  IX,  No.  4,  p.  588. 


BIBLIOGRAPHY  87 

33.  A  New  Method  of  Constructing  Volume  Tables  (By  Frustum  Form  Factors).     Donald 

Bruce,  Forestry  Quarterly,  Vol.  X,  No.  2,  p.  215. 

34.  Use  of  Frustum  Form  Factors  for  Constructing  Volume  Tables.      Donald  Bruce,  Proceed- 

ings of  the  Society  of  American  Foresters,  Vol.  VIII,  No.  3,  p.  27S. 

35.  Taper  Curves  in  Relation  to  Linear  Products.     F.  S.  Baker,  Proceedings  of  the  Society  of 

American  Foresters,  Vol.  IX,  No.  3,  p.  380. 

36.  Graded  Volume  Tables  for  Vermont  Hardwoods.      I.  W.  Bailey  and  P.  C.  Heath,  Forestry 

Quarterly,  Vol.  XII,  No.  1,  p.  5. 

37.  Multiple  Volume  Table.     Lincoln  Crowell,  Forestry  Quarterly,  Vol.  IX,  No.  2,  p.  261. 

38.  Construction  of  a  Set  of  Taper  Cvirves.      W.  B.  Barrows,  Proceedings  of  the  Society  of 

American  Foresters,  Vol.  X,  No.  1,  p.  32. 

39.  Reading  and  Replotting  Curves.      W.  B.  Barrows,  Proceedings  of  the  Society  of  American 

Foresters,  Vol.  X,  No.  1,  p.  65. 

40.  Top  Diameters  as  Affecting  the  Frustum  Form  Factor  for  Longleaf  Pine.      H.  H.  Chapman, 

Proceedings  of  the  Society  of  American  Foresters,  Vol.  XI,  No.  2,  p.  185. 

41.  Logarithmic    Cross-section    Paper    in    Forest    Mensuration.      Donald    Bruce,    Journal    of 

Forestry,  Vol.  XV,  No.  3,  p.  335. 

42.  The  Problem  of  Making  Volume  Tables  for  Use  on  the  National  Forests.     T.  T.  Munger, 

Journal  of  Forestry,  Vol.  XV,  No.  5,  p.  574. 

43.  A  Volume  Table  for  Hewed  Railroad  Ties.     J.  W.  Girard  and  U.  S.  Swartz.     Journal  of 

Forestry,  Vol.  XVII,  No.  7,  p.  839. 

44.  The  Height  and  Diameter  Basis  for  Volume  Tables.     Donald  Bruce,  Journal  of  Forestry, 

Vol.  XVIII,  No.  5,  p.  549. 

SCALING 

45.  Scaling  Regulations.     The  National  Forest  Manual,  Forest  Service,  U.  S.  Department  of 

Agriculture,  Washington,  D.  C. 

46.  History  and  Evolution  of  Scaling.     American  Lumberman,  December  24,  1910,  p.  29. 

47.  Scaling  Government  Timber.     T.  S.  Woolsey,  Forestry  Quarterly,  Vol.  V,  No.  2,  p.  166. 

48.  Method   Making  Discounts  for   Defects.      H.   D.   Tieman,   Forestry   Quarterly,   Vol.   Ill, 

No.  4,  p.  354. 

49.  General  Regulations  Concerning  Scaling  in  British  Columbia.     Andrew  Haslam,  Proceed- 

ings of  the  Second  Pacific  Logging  Congress,  p.  23. 

50.  Red  and  White  Fir  Xylometer  Cordwood  Test.     Taylor,   Forestry  Quarterly,  Vol.  XII, 

No.  1,  p.  24. 

51.  Factors  Influencing  the  Volume  of  Wood  in  a  Cord.      Raphael  Zon,  Forestry  Quarterly, 

Vol.  I,  No.  4,  p.  126. 

52.  British  Columbia  Log  Grades.     West  Coast  Lumberman,  March  15,  1914,  p.  32. 

53.  Early  History  of  Log  Scaling  Practice.      C.  E.  Knouf,  West  Coast  Lumberman,  July  15, 

1920,  p.  41  and  August  1.  1920,  p.  40. 

54.  Log  Scaling  in  Douglas  Fir  Region.      E.  I.  Karr,  The  Timberman,  April,  1920,  p.  32o. 

DETERMINATION  OF  THE  CONTENTS  OF  STANDS 

55.  A  Manual  for  Northern  Woodsmen.     Cary,  Published  by  Harvard  University,  Cambridge, 

Mass.,  1901. 

56.  Average  Log  Cruise  (Spaulding  Rule  Method).     W.  J.  Ward,  Forestry  Quarterly,  Vol.  V, 

No.  3,  p.  268. 

57.  Errors  in   Estimating   Timber.      Louis   Margolin,    Forestry   Quarterly,    Vol.    XII,    No.   2, 

p.  167. 


88  APPENDIX 

58.  A  Method  of  Estimating.     Clyde  Leavitt,  Forestry  Quarterly,  Vol.  II,  No.  3,  p.  161. 

59.  Forest  Service  Method  of  Check  Cruising.      Editorial,  The  Timberman,  November,  1913, 

p.  25. 

60.  A  Short  Cut  Method  of  Cruising.     C.  S.  Judd,  Forestry  Quarterly,  Vol.  XI,  No.  3,  p.  380. 

61.  Timber  Estimating.      H.  H.  Chapman,  Proceedings  of  the  Society  of  American  Foresters, 

Vol.  IV.  No.  1,  p.  114. 

62.  The  Factor  of  Top  Diameter  in  Construction  and  Application  of  Volume  Tables  Based  on 

Log  Lengths.      H.   II.   Chapman,   Proceedings   of   the   Society  of  American   Foresters, 
Vol.  XI,  No.  2,  p.  221. 

63.  Timber  Estimating  in  the  South  Appalachians.      R.  C.  Hall,  Journal  of  Forestry,  Vol.  XV, 

No..  3s  p.  310. 

64.  A  Formula  Method  for  Estimating  Timber.     E.  I.  Terry,  Journal  of  Forestry,  Vol.  XVII, 

No.  4,  p.  413. 

65.  Comment  on  "A  Formula  Method  of  Estimating  Timber."      Donald  Bruce,  Journal  of 

Forestry,  Vol.  XVII,  No.  5,  p.  691. 


GROWTH  AND  YIELD  STUDIES 

66.  Suggestions  on  Predicting  Growth  for  Short  Periods.     J.  C.  Stetson,  Forestry  Quarterly, 

Vol.  VIII,  No.  3,  p.  326. 

67.  Growth  of  Red  Pine  in  Ontario.     A.  H.  D.  Ross,  Forestry  Quarterly,  Vol.  XI,  No.  2,  p.  160. 

68.  Use  of  Yield  Tables  in  Predicting  Growth.     E.  E.  Carter,  Proceedings  of  the  Society  of 

American  Foresters,  Vol.  IX,  No.  2,  p.  177. 

69.  Measurement  of  Increment  in  All-aged  Stands.      H.  H.  Chapman,  Proceedings  of  the  Society 

of  American  Foresters,  Vol.  IX,  No.  2,  p.  189. 

70.  Determination   of   Stocking  in   Uneven-aged   Stands.     W.   W.   Ashe,   Proceedings   of   the 

Society  of  American  Foresters,  Vol.  IX,  No.  2,  p.  204. 

71.  Determination  of  Site  Qualities  for  Even-aged  Stands  by  Site  Factors.      E.  J.  Hanzlick, 

Proceedings  of  the  Society  of  American  Foresters,  Vol.  IX,  No.  2,  p.  229. 

72.  Permanent  Sample  Plots.     T.  S.  Woolsey,  Forestry  Quarterly,  Vol.  X,  No.  1,  p.  38. 

73.  Method  of  Calculating  Yield  in  India.     A.  D.  Blaschock,  Forestry  Quarterly,  Vol.  VIII, 

No.  3,  p.  330. 

74.  Determination  of  Quality  of  Locality  by  Fibre  Length  of  Wood.     C.   D.   Mell,  Forestry 

Quarterly,  Vol.  VIII,  No.  4,  p.  419. 

75.  Yield  in  Uneven-aged  Stands.      Barrington  Moore,  Proceedings  of  the  Society  of  American 

Foresters,  Vol.  IX,  No.  2,  p.  216. 

76.  Relation  of  Crown  Space  to  Volume  of  Present  and  Future  Yellow  Pine  Stands.      Kerr, 

Forestry  Quarterly,  Vol.  XII,  No.  3,  p.  330. 

77.  Method    for    Regulating    the    Yield    in    Selection    Forests.     Walter    J.    Morrill,    Forestry 

Quarterly,  Vol.  XI,  No.  1,  p.  21. 

78.  Methods    of    Investigating   Yields   in    Many-aged    Stands.     H.    H.    Chapman,    Forestry 

Quarterly,  Vol.  X,  No.  3,  p.  458. 

79.  Coordination  of  Growth  Studies,   Reconnaissance  and   Regulation  of  Yield  on   National 

Forests.     H.  H.  Chapman,  Proceedings  of  the  Society  of  American  Foresters,  Vol.  VIII, 
No.  3,  p.  317. 

80.  Stem  Analysis.     John  Bentley,  Jr.,  Forestry  Quarterly,  Vol.  XII,  No.  2,  p.  158. 
SI.   Increment  Measurements.     Brief,  Forestry  Quarterly,  Vol.  XIII,  No.  4,  p.  550. 

82.   Notes  on  a  Method  of  Studying  Growth  Per  cent.      B.  A.  Chandler,  Forestry  Quarterly, 
Vol.  XIV,  No.  3,  p.  453. 


UNITS  OF  MEASUREMENT 


89 


S3.   Plan  for  Permanent  Sample  Plots  in  the  Adirondacks.     Journal  of  Forestry,   Vol.   XVI, 

No.  8,  p.  922.     S.  N.  Spring,  et  al. 
84.   A  Simplified  Method  of  Stem  Analysis.     T.  W.   Dwight,  Journal  of  Forestry,  Vol.   XV, 

No.  7,  November,  1917,  p.  8G4. 
8.5.   Mechanical  Aids  in  Stem  Analysis.     Ernest  C.   Pegg,   Journal  of  Forestry,   Vol.    XVII, 

No.  6,  October,  1919,  p.  682. 
86.  Classifying  Forest  Sites  by  Height  Growth.     E.   H.  Frothingham,  Journal  of  Forestry, 

Vol.  XIX,  No.  4,  April,  1921,  p.  374. 

UNITS  OF  MEASUREMENT 

Used  in  Land  Surveying  and  Forest  Mensuration 
1   Mile 
5280  feet 

80  chains  (66  feet  each) 
320  rods  (16^  feet  each) 
16  tallies  (5  chains  each) 
1000  standard  double  paces  (5.  28  feet) 
2000  standard  single  paces    (2 .  64  feet) 

1  Acre 
43,560  square  feet 
10  square  chains 
160  square  rods 

2  chain  strip,  1  tally  in  length 

-1  Section 
640  acres 
16  "forties"  (square  forty  acre  tracts) 
1  mile  square 

DIMENSIONS  OF  FRACTIONAL  ACRE  TRACT 


Size  of  Fractional 
Tract 

(Acres) 


Area  of  Fractional 

Length  of  Side 

Tract 

if  Square 

(Square  Feet) 

(Feet) 

43,560 

208.7 

21,780 

147.6 

10,890 

104.4 

5,445 

73.1 

2,722.5 

52.2 

Length  of  Radius 

if  Circular 

(Feet) 


117.8 
83.3 
58.9 
41.6 
29.4 


90 


APPENDIX 


MENSURATION   FORMS 
Form   1 


i      i 


I  I 


MENSURATION   FORMS 

Form  2A 


91 


Series Species . . 

Locality S . 


M 


Regular 

Volume 

Measurements 

As  Used  by  Logger 

< 

it 

\'olume 

t-3 

p 

> 

1 

St 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

1? 

13 

14 

15 

16 

17 

18 

19 

26 



Tree  No . 


SUMMARY 


Plot  No . 


3  « 


Volume, 
B.M. 


s§ 


Name 


Date 


92 


APPENDIX 


2 

T 

t^ 

3 
O 

3 

O 

o 

a 

3 

rjj 

1 

CO 

T 

(M 

5 
O 

- 

2 
2 

O 

a 

o 

Li 

3 

'i 

05 

oo 

- 

CD 

o 
o 

3 

lO 

-3 

5 

-f 

fO 

(N 

- 

c 

=1 

""a 

c^ 

cc 

t 

IT 

t^ 

X 

c- 

c 

- 

^ 

't 

15 

u  s 


MENSURATION   FORMS 


93 


P'ORM    3A 
UNITED    STATES   DEPARTMENT   OF   AGRICULTURE 

FOREST   SERVICE 

D-6  DOUGLAS  FIR  REGION 

TIMBER   SURVEY    TALLY    SHEET 
N 


Form  494— D  6b 
(Revised,  1917) 


4 

3 

2 

1 

5 

'^ 

s^ 

8 

12 

11  s 

r^io 

9 

13 

14 

15 

16 

Ht.  Class Site . 


R W     Compassman  . 

Estimator.  .  . 

Sec Date 

40  No f 

Est.  \ 
Sheet [  Tot.. 


19. 


Applies  to  { 
Acres  Tot. 


D.B.H. 

D.F. 

1               '               '               ^ 

D.B.H. 

D.F. 

10-14 

1 

1 
i 

54 

16 

1 
1 

56 

18 

58 

20 

60 

22 

62 

24 

64 

26 

66 

28 

68 

30 

70 

32 

72 

34 

74 

36 

76 

38 

78 

40 

80 

42 

Sound,  D.F. 

44 

Def..  D.F. 

46 

Total 

48 

Snags  over  30  ft.  tall 

50 

i 

D.B.H. 

52 

20-36 

Gross  vol. 
on  strip 

37-48 

Cull  %     B 
D 

49  up 

Vol.  strip 
Net 

No.  per  A. 

Vol.  on  40 
Net 

Avei 
stand  T 

age 
3er  A. 

94 


APPENDIX 


Form  3B 


Forest  Types:    

Age  Classes:    

Condition  of  Timber: 

Thrifty 

Mature 

Decadent 

Fire  killed 


%. 
■  %. 
% ;      damaged . 


Insect  killed % ;      damaged  . 

Other  killed % ;      damaged  . 

Name  of  disease 

Species  affected 


Quality  of  Timber: 

[Give  by  log  grade;    percentage  of  tall,  medium,  or  short  clear  boles;    or  number  of  clear 
logs  of  stated  minimum  length  and  diameter.] 


Logging  factors: 

Undergrowth — Light,  medium,  dense. 

Wind  fall — Light,  medium,  dense. 

Boulders  and  broken  rock — Numerous,  occasional,  absent. 

Other  factors 

Reproduction:  Speciea. 

No  reproduction 

Ground  J  stocked 

Ground  §  stocked 

Ground  fully  stocked 

Additional  Notes: 


Per  cent. 


MENSURATION     FORMS 


95 


Form   1A 


Douglas 

Fir 

Western  Red  Cedar 

D.B. 
H. 

to 
75 

76 
to 
105 

106 
to 
135 

136 
to 
165 

166 
to 
195, 

etc. 

to 
75 

76 
to 
105 

106 
to 
135 

136 
to 
165 

166 
to 
195, 

etc. 

to 
75 

76 
to 
105 

106 

to 

135 

136 
to 
165 

166 
to 
195, 

etc. 

14 

• 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

40 

42 

44 



46 

48 

50 

52 

54 

56 

58 

60 

62 

64 



66 

68 



70 

72 

74  ! 

96  APPENDIX 

Form  4J} 

Acre  No Sec T 

Course Offset Ch's from 

Compassman Date 


Cruiser 

Per  rent  of  eruise 
Width  of  strip .  .  . 


Type 


Slope 


Asoect 


FOREST    DESCRIPTION 


Rock 


Soil 


Humus 


Ground  Cover 


Undergrowth 


Reoroduction 


Density 


Quality  of  Locality 


Condition  of  Stand 


Age  of  Stand 
Remarks 


MENSURATION   FORIMS 


97 


Form   5 

Locality Brand . 

Where  Scaled Date  . 


Log 

1 

5 

a 

Contents  by  Species 

Defects,  Kind, 

No. 

Doug. 
Fir 

Hem- 
lock 

Cedar 

Amount  Deducted, 
Overlengths 

1 

i 

1 

1 
i 

1 

1 

1 

1 
1 

0 

II 

1 

3 

>> 

c 
a 

u 

1 

Totals 

for 
Page 

1 

i 

APPENDIX 


COLUMBIA    RIVER    L(3G   SCALING    AND    GRADING    BUREAU    LOG 
GRADING  RULES  FOR  DOUGLAS  FIR 

No.  1  Logs. 

No.  1  logs  shall  be  logs  which,  in  the  judgment  of  the  scaler,  will  be  suitable 
for  the  manufacture  of  lumber  in  the  grades  of  No.  2  clear  or  better  to  an  amount 
of  not  less  than  50  per  cent  of  the  scaled  contents. 

No.  1  logs  shall  contain  not  less  than  six  annual  rings  to  the  inch  in  the 
outer  portion  of  the  log  equal  to  one-half  of  the  log  content;  and  No.  1  logs  shall 
be  straight  grained  to  the  extent  of  a  variation  of  not  more  than  2  inches  to 
the  lineal  foot  for  a  space  of  6  lineal  feet  equidistant  from  each  end  of  the  log. 

Rings,  rot,  or  any  defect  that  may  be  eliminated  in  the  scale,  are  permitted 
in  a  No.  1  log  providing  their  size  and  location  do  not  prevent  the  log  pro- 
ducing the  required  amount  of  No.  2  clear  or  better  lumber. 

A  No.  1  log  may  contain  a  few  small  knots  or  well  scattered  pitch  pockets 
as  permitted  in  grades  of  No.  2  clear  or  better  lumber;  or  may  contain  a  very 
few  grade  defects  so  located  that  they  do  not  prevent  the  production  of  the 
required  amount  of  clear  lumber. 

No.  2  Logs. 

No.  2  logs  shall  not  be  less  than  12  feet  in  length,  having  defects  which 
prevent  their  grading  No.  1,  but  which,  in  the  judgment  of  the  scaler,  will  be 
suitable  for  the  manufacture  of  lumber  principally  in  the  grades  of  No.  1 
common  or  better. 

No.  3  Logs. 

No.  3  logs  shall  be  not  less  than  12  feet  in  length,  having  defects  which 
prevent  their  grading  No.  2  but  which,  in  the  judgment  of  the  scaler,  will  be 
suitable  for  the  manufacture  of  inferior  grades  of  lumber. 

Cull  Logs. 

Cull  logs  shall  be  any  logs  which  do  not  contain  33^  per  cent  of  sound  lumber. 


PUGET  SOUND   GRADING   RULES  99 


PUGET     SOUND     LOGGERS     ASSOCL\TION     LOG     SCALING     AND 

GRADING  RULES  FOR  DOUGLAS  FIR 
A^o.  1  Logs. 

No.  1  logs  shall  be  logs  in  the  lengths  of  16  to  32  feet  and  30  inches  in 
diameter  inside  the  bark  at  the  small  end  and  logs  34  to  40  feet,  28  inches  in 
diameter  inside  the  bark  at  the  small  end,  and  shall  be  logs  which  in  the  judg- 
ment of  the  scaler  shall  contain  at  least  50  per  cent  of  the  scaled  contents,  in 
lumber  in  the  grades  of  No.  2  clear  and  better. 

No.  2  Logs. 

No.  2  logs  shall  be  not  less  than  16  feet  long  and  having  defects  which 
prevent  its  grading  No.  1,  but  which  in  the  judgment  of  the  scaler  will  be 
suitable  for  the  manufacture  of  lumber  principally  in  the  grades  of  merchant- 
able and  better. 

No.  3  Logs. 

No.  3  logs  shall  be  not  less  than  16  feet  long  and  having  defects  which  pre- 
vent its  cutting  into  higher  grades  and  in  the  judgment  of  the  scaler  will  be 
suitable  for  the  manufacture  of  common  lumber. 

Cull  Logs. 

Cull  logs  shall  be  any  logs  which  in  the  judgment  of  the  scaler  will  not  cut 
33^  per  cent  of  sound  lumber. 


100 


AI'PENDIX 


1ABLES 

TABLE   I 
ScHiFFEL  Formula  D.B.H.  Basal  Areas,  0.16  of  the  Area  of  a  Circle  at  Breast  Height 


Diam- 

0.0 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

eter, 

Square 

Square 

S(iuare 

S(iuare 

Square 

Square 

Square 

Square 

Square 

Sciuare 

Inches 

Feet 

Feet 

Feet 

Feet 

Feet 

Fee:: 

Feet 

Feet 

Feet   . 

Feet 

1 

0.001 

0.001 

0.001 

0.001 

0.002 

0.002 

0.002 

0.003 

0.003 

0.003 

2 

0.003 

0.004 

0.004 

0.005 

0.005 

0.005 

0.006 

0.006 

0.007 

0.007 

3 

0.008 

0.008 

0.009 

0.010 

0.010 

0.011 

0.011 

0.012 

0.013 

0.013 

4 

0.014 

0.015 

0.016 

0.017 

0.018 

0.018 

0.018 

0.019 

0.020 

0.021 

5 

0.022 

0.083 

0.024 

0.025 

0 .  025 

0.026 

0.027 

0.02S 

0.029 

0 .  030 

6 

0.031 

0.032 

0.034 

0.035 

0.036 

0.037 

0.038 

0.039 

0.040 

0.042 

7 

0.043 

0.044 

0.045 

0.047 

0.048 

0.049 

0.050 

0.052 

0.053 

0.054 

8 

0.056 

0.057 

0.059 

0.060 

0 .  062 

0.063 

0 .  065 

0.066 

0.068 

0.069 

9 

0.071 

0.072 

0.074 

0.075 

0.077 

0.079 

0.080 

0.082 

0.084 

0.086 

10 

0.087 

0.089 

0.091 

0.093 

0.094 

0.096 

0.098 

0.100 

0.102 

0.104 

11 

0.106 

0.108 

0.109 

0.111 

0.113 

0.115 

0.117 

0.119 

0.122 

0.124 

12 

0.126 

0.128 

0.130 

0.132 

0.134 

0.136 

0.139 

0.141 

0.143 

0.145 

13 

0.147 

0.150 

0.152 

0.154 

0.157 

0.159 

0.161 

0.164 

0.166 

0.169 

14 

0.171 

0.173 

0.176 

0.178 

0.181 

0.183 

0.186 

0.189 

0.191 

0.194 

15 

0.196 

0.199 

0.202 

0.204 

0.207 

0.210 

0.212 

0.215 

0.218 

0.221 

If) 

0 .  223 

0.226 

0.229 

0.232 

0.235 

0.238 

0.240 

0.243 

0.246 

0.249 

17 

0.252 

0 .  255 

0.258 

0.261 

0.264 

0.267 

0.270 

0.273 

0.276 

0.280 

18 

0.283 

0.286 

0.289 

0.292 

0.295 

0.299 

0 .  302 

0.305 

0.308 

0.312 

19 

0.315 

0.318 

0.322 

0.325 

0.328 

0.332 

0.335 

0.339 

0.342 

0.346 

20 

0.349 

0.353 

0.356 

0.360 

0.363 

0.367 

0.370 

0.374 

0.378 

0.381 

21 

0.385 

0.389 

0.392 

0.396 

0.400 

0.403 

0.407 

0.411 

0.415 

0.419 

22 

0.422 

0.426 

0.430 

0.434 

0.438 

0.442 

0.446 

0.450 

0.454 

0.458 

23 

0.462 

0.466 

0.470 

0.474 

0.478 

0.482 

0.486 

0.490 

0 .  494 

0.498 

24 

0.503 

0.507 

0.511 

0.515 

0.520 

0.524 

0.528 

0.532 

0.537 

0.541 

25 

0.545 

0.550 

0.554 

0.559 

0.563 

0.567 

0.572 

0.576 

0.581 

0.585 

2G 

0.590 

0,594 

0.599 

0 .  604 

0.608 

0.613 

0.617 

0.622 

0.627 

0.631 

27 

0.636 

0.641 

0.646 

0 .  650 

0 .  655 

0.()60 

0 .  665 

0.670 

0.674 

0 .  679 

28 

0 .  684 

0.689 

0.694 

0.699 

0.704 

0.709 

0.714 

0.719 

0.724 

0.729 

29 

0.734 

0.739 

0.744 

0.749 

0.754 

0.759 

0.765 

0.770 

0.775 

0.780 

30 

0.785 

0.791 

0.796 

0.801 

0.806 

0.812 

0.817 

0.822 

0.828 

0.833 

31 

0.839 

0.844 

0.849 

0.855 

0.860 

0.868 

0.871 

0.877 

0.882 

0.888 

32 

0.894 

0.899 

0.905 

0.910 

0.916 

0.922 

0.927 

0.933 

0.939 

0.945 

33 

0.950 

0.956 

0.962 

0.968 

0.974 

0.979 

0.985 

0.991 

0.997 

1.003 

34 

1.009 

1.015 

1.021 

1.027 

1.033 

1 .  039 

1 .  045 

1.051 

1 .  057 

1.063 

35 

1.069 

1.075 

1.081 

1 .  087 

1.094 

1.100 

1.106 

1.112 

1.118 

1.125 

36 

1.131 

1 .  137 

1.144 

1 .  150 

1 .  156 

1 .  163 

1.169 

1.175 

1.182 

1.188 

37 

1 .  195 

1.201 

1.208 

1.214 

1.221 

1.227 

1.234 

1.240 

1.247 

1.254 

38 

1.260 

1.267 

1.273 

1.280 

1.287 

1.294 

1.300 

1 .  307 

1.314 

1.321 

39 

1.327 

1 .  334 

1.341 

1 .  348 

1 .  355 

1.362 

1.368 

1.375 

1.382 

1.389 

40 

1 .  396 

1 .  403 

1.410 

1.417 

1.424 

1.431 

1 

1.438 

1.446 

1.453 

1.460 

TABLES 


101 


TABLE    I— Continued 


Diam- 

0.0 

o;i 

0. 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

eter, 

Square 

Square 

Square 

Square 

Square 

Square 

Square 

Square 

Square 

Square 

Inches 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

41 

1.467 

1.474 

1.481 

1.488 

1.496 

1.503 

1.510 

1.517 

1.525 

1.532 

42 

1.539 

1.547 

1.554 

1.561 

1.569 

1.576 

1.584 

1.591 

1.599 

1.606 

43 

1.614 

1.621 

1.629 

1.636 

1.644 

1.651 

1.659 

1.667 

1.674 

1.682 

44 

1.689 

1.697 

1.705 

1.713 

1.720 

1.728 

1.736 

1.744 

1.751 

1.759 

45 

1.767 

1.775 

1.783 

1.791 

1.799 

1.807 

1.815 

1 .  823 

1.831 

1.839 

46 

1.847 

1.855 

1.863 

1.871 

1.879 

1.887 

1.895 

1.903 

1.911 

1.920 

47 

1.928 

1.936 

1.944 

1.952 

1.961 

1.969 

1.977 

1.986 

1.994 

2.002 

48 

2.011 

2.019 

2.027 

2.037 

2.044 

2.053 

2.061 

2.070 

2.078 

2.087 

49 

2.095 

2.104 

2.112 

2.121 

2.130 

2.138 

2.147 

2.156 

2.164 

2.173 

50 

2.182 

2.190 

2.199 

2.208 

2.217 

2.226 

2.234 

2.243 

2.252 

2.261 

51 

2.270 

2.279 

2.288 

2.297 

2.306 

2.315 

2.324 

2 .  333 

2.342 

2.351 

52 

2.360 

2.369 

2.378 

2.387 

2.396 

2.405 

2.414 

2.424 

2.433 

2.442 

53 

2.451 

2.461 

2.470 

2.479 

2.488 

2.498 

2.507 

2.516 

2.526 

2.535 

54 

2.545 

2.554 

2.564 

2.573 

2.583 

2.592 

2.602 

2.611 

2.621 

2.630 

55 

2.640 

2.649 

2.659 

2.669 

2.678 

2.688 

2.698 

2.707 

2.717 

2.727 

56 

2.737 

2.746 

2.756 

2.766 

2.776 

2.786 

2.796 

2.806 

2.815 

2.825 

57 

2.835 

2.845 

2.855 

2.865 

2.875 

2.885 

2.895 

2.905 

2.915 

2.926 

58 

2.936 

2.946 

2.956 

2.966 

2.976 

2.986 

2.997 

3.007 

3.017 

3.027 

59 

3.038 

3.048 

3.058 

3.069 

3.079 

3.089 

3.100 

3.110 

3.121 

3.131 

60 

3.142 

3.152 

3.163 

3.173 

3.184 

3.194 

3.205 

3.215 

3.226 

3.237 

61 

3.247 

3.258 

3.269 

3.279 

3.290 

3.301 

3.311 

3.322 

3.333 

3.344 

62 

3.355 

3.365 

3.376 

3.387 

3.398 

3.409 

3.420 

3.431 

3.442 

3.453 

63 

3.464 

3.475 

3.486 

3.497 

3.508 

3.519 

3.530 

3.541 

3.552 

3.563 

64 

3.574 

3.586 

3.597 

3.608 

3.619 

3.630 

3.642 

3.653 

3.664 

3.676 

65 

3.687 

3.698 

3.710 

3.721 

3 .  733 

3./'44 

3.755 

3.767 

3.778 

3.790 

66 

3.801 

3.813 

3.824 

3.836 

3.848 

3.859 

3.871 

3 .  882 

3 .  894 

3.906 

67 

3.917 

3.929 

3.941 

3.953 

3.964 

3.976 

3.988 

4.000 

4.012 

4.023 

68 

4.035 

4.047 

4.059 

4.071 

4.083 

4.095 

4.107 

4.119 

4.131 

4.143 

69 

4.155 

4.167 

4.179 

4.191 

4.203 

4.215 

4.227 

4.239 

4.252 

4.264 

70 

4.276 

4.288 

4.301 

4.313 

4.325 

4.337 

4.350 

4.362 

4.374 

4.387 

71 

4.399 

4.412 

4.424 

4.436 

4.449 

4.461 

4.474 

4.486 

4.499 

4.511 

72 

4.524 

4.536 

4.549 

4.562 

4.574 

4.587 

4.600 

4.612 

4.625 

4.638 

73 

4 .  650 

4.663 

4.676 

4.689 

4.702 

4.714 

4.727 

4.740 

4.753 

4.766 

74 

4  779 

4.792 

4.805 

4.818 

4.831 

4.844 

4.857 

4.870 

4.883 

4.896 

75 

4.909 

4.922 

4.935 

4.948 

4.961 

4.975 

4.988 

5.001 

5.014 

5.027 

76 

5.041 

5.054 

5.067 

5.080 

5.094 

5.107 

5.120 

5.134 

5.147 

5.161 

77 

5.174 

5.187 

5.201 

5.214 

5.228 

5.241 

5.255 

5.269 

5.282 

5.296 

78 

5 .  309 

5.323 

5.337 

5.350 

5.364 

5.378 

5.391 

5.405 

5.419 

5.433 

79 

5.446 

5.460 

5.474 

5.488 

5.502 

5.515 

5.529 

5.543 

5.557 

5.571 

80 

5.585 

5 .  599 

5.613 

5.627 

5.641 

5.655 

5.669 

5.683 

5.697 

5.711 

102 


APPENDIX 


TABLE    II 

ScHiFFEL  Formula  Middle  Diametek  Basal  Areas,  0.G6  of  tue  Area  of  a  Circle  at 
THE  Middle  Height  of  the  Tree 


Diam- 

0.0 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

eter, 

Square 

Square 

Square 

Square 

Square 

Square 

Square 

Square 

Square 

Square 

Inches 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet, 

I'eet 

1 

0.004 

0.004 

0.005 

0.006 

0.007 

0.008 

0.009 

0.010 

0.012 

0.013 

2 

0.014 

U.016 

0.017 

0.019 

0.021 

0.023 

0.024 

0 .  026 

0.028 

0 .  030 

3 

0.032 

0.035 

0.037 

0.039 

0.042 

0.044 

0.047 

0 .  049 

0.052 

0 .  055 

4 

0.058 

0.061 

0.064 

0.067 

0.070 

0.073 

0.076 

0.080 

0.083 

0.086 

5 

0.090 

0 .  094 

0.097 

0.101 

0.105 

0.109 

0.113 

0.117 

0.121 

0.125 

6 

0.130 

0.134 

0.138 

0.143 

0.147 

0.152 

0.157 

0.162 

0.166 

0.171 

7 

0.176 

0.182 

0.187 

0.192 

0.197 

0.202 

0.208 

0.213 

0.219 

0.225 

8 

0.230 

0.236 

0.242 

0.248 

0.254 

0.260 

0.266 

0.273 

0.279 

0.285 

9 

0.292 

0.29S 

0.305 

0.311 

0.318 

0.325 

0.332 

0.339 

0.346 

0.353 

10 

0.360 

0.367 

0.375 

0.382 

0.389 

0.397 

0.405 

0.412 

0.420 

0.428 

11 

0.436 

0.444 

0.452 

0.460 

0.468 

0.476 

0.484 

0.493 

0.501 

0.510 

12 

0.518 

0.527 

0.536 

0.545 

0.554 

0.563 

0.572 

0.581 

0.590 

0 .  599 

13 

0.608 

0.618 

0.627 

0.637 

0.646 

0.656 

0.666 

0.676 

0.686 

0.696 

14 

0.706 

0.716 

0.726 

0.736 

0.746 

0.757 

0.767 

0.778 

0.788 

0.799 

15 

0.810 

0.821 

0.832 

0.843 

0.854 

0.865 

0.876 

0.887 

0.899 

0.910 

16 

0.922 

0.933 

0.945 

0.956 

0.968 

0.980 

0.992 

1.004 

1.016 

1.028 

17 

1.040 

1.053 

1.065 

1.077 

1.090 

1.102 

1.115 

1.128 

1.140 

1.153 

18 

1.166 

1.179 

1.192 

1 .  205 

1.219 

1.232 

1.245 

1.259 

1.272 

1.286 

19 

1.299 

1.313 

1.327 

1.341 

1.355 

1.369 

1.383 

1.397 

1.411 

1.426 

20 

1.440 

1 .  454 

1.469 

1.483 

1.498 

1.513 

1.528 

1.542 

1.557 

1.572 

21 

1.587 

1.603 

1.618 

1 .  633 

1.649 

1.664 

1.680 

1.695 

1.711 

1.726 

22 

1.742 

1.758 

1.774 

1.790 

1.806 

1.822 

1.839 

1.855 

1.871 

1.888 

23 

1.904 

1.921 

1.937 

1.954 

1.971 

1.988 

2.005 

2.022 

2.039 

2.056 

24 

2.073 

2.091 

2.108 

2.126 

2.143 

2.161 

2.178 

2.196 

2.214 

2.232 

25 

2.250 

2.268 

2.286 

2.304 

2.322 

2.341 

2.359 

2.378 

2.396 

2.415 

26 

2.433 

2.452 

2.471 

2.490 

2.509 

2.528 

2.547 

2 .  566 

2.585 

2.605 

27 

2.624 

2.644 

2.663 

2.683 

2.703 

2.722 

2.742 

2.762 

2.782 

2.802 

28 

2.822 

2.842 

2.863 

2.883 

2.903 

2.924 

2.944 

2.965 

2.986 

3.006 

29 

3.027 

3.048 

3.069 

3 .  090 

3.111 

3.133 

3.154 

3.175 

3.197 

3.218 

30 

3 .  240 

3.261 

3 .  283 

3.305 

3.327 

3.349 

3.371 

3.393 

3.415 

3.437 

31 

3.459 

3 .  482 

3.504 

3.527 

3.549 

3.572 

3 .  595 

3.617 

3.640 

3.663 

32 

3.686 

3.709 

3 .  732 

3.756 

3.779 

3 .  802 

3.826 

3.849 

3.873 

3.896 

33 

3.920 

3.944 

3.968 

3.992 

4.016 

4.040 

4.064 

4.088 

4.112 

4.137 

34 

4.161 

4.186 

4.210 

4.235 

4.260 

4.285 

4.309 

4 .  334 

4.359 

4.385 

35 

4.410 

4.435 

4.460 

4.486 

4.511 

4.537 

4.562 

4.588 

4.614 

4.639 

36 

4.665 

4.691 

4.717 

4.743 

4.769 

4.796 

4.822 

4.848 

4.875 

4.901 

37 

4.928 

4.955 

4.981 

5.008 

5.035 

5.062 

5.089 

5.116 

5.143 

5.171 

38 

5.198 

5 .  225 

5.253 

5 .  280 

5.308 

5.336 

5.363 

5.391 

5.419 

5.447 

39 

5.475 

5.503 

5.532 

5 .  560 

5.588 

5.616 

5.645 

5.673 

5 .  702 

5.731 

40 

5.760 

5.788 

5.817 

5.846 

5.875 

5.904 

5.934 

5.963 

5.992 

6.022 

41 

6.051 

6.081 

6.110 

6.140 

6.170 

6.200 

6.230 

6.260 

6.290 

6  320 

42 

6.350 

6.380 

6.411 

6.441 

6.471 

6.502 

6.533 

6.563 

6.594 

6.625 

43 

6.656 

6 .  687 

6.718 

6.749 

6.780 

6.812 

6.843 

6.874 

6.906 

6.937 

44 

6 .  969 

7.001 

7.033 

7.064 

7.096 

7.128 

7.160 

7.193 

7 .  225 

7.257 

45 

7.290 

7 .  322 

7.354 

7 .  387 

7.420 

7.452 

7.485 

7.518 

7.551 

7 .  584 

46 

7.617 

7.650 

7 .  683 

7.717 

7.750 

7.784 

7.817 

7.851 

7.884 

7.918 

47 

7 .  952 

7 .  986 

8.020 

8.054 

8.088 

8.122 

8.156 

8.190 

8 .  225 

8.259 

48 

8.294 

8.328 

8.363 

8.404 

8.433 

8.467 

8.502 

8.537 

8.573 

8.608 

49 

8.643 

8.678 

8.714 

8.749 

8.785 

8.820 

8.856 

8.892 

8.927 

8.963 

50 

8.999 

9.035 

9.072 

9.108 

9.144 

9.180 

9.217 

9.253 

9.290 

9.326 

TABLES 


103 


TABLE    III 
Areas  of  Circles  for  Diameters  of  1  Inch  to  60  Inches 


Diam- 

Area, 

Diam- 

Area, 

Diam- 

Area, 

Diam- 

Area, 

Diam- 

Area, 

Diam- 

Area, 

eter, 

Square 

eter, 

Square 

eter, 

Square 

eter, 

Square 

eter, 

Square 

eter, 

Square 

Inches 

Feet 

Inches 

Feet 

Inches 

Feet 

Inches 

Feet 

Inches 

Feet 

Inches 

Feet 

1.0 

0.006 

5.0 

0.136 

9.0 

0.442 

13.0 

0.922 

17.0 

1.576 

21.0 

2.405 

1.1 

0.007 

5.1 

0.142 

9.1 

0.452 

13.1 

0.936 

17.1 

1.595 

21.1 

2.428 

1.2 

0.008 

5.2 

0.147 

9.2 

0.462 

13.2 

0.950 

17.2 

1.614 

21.2 

2.451 

1,3 

0.009 

5.3 

0.153 

9.3 

0.472 

13.3 

0.965 

17.3 

1.632 

21.3 

2.475 

1.4 

0.011 

5.4 

0.159 

9.4 

0.482 

13.4 

0.979 

17.4 

1.651 

21.4 

2.498 

1.5 

0.012 

5.5 

0.165 

9.5 

0.492 

13.5 

0.994 

17.5 

1.670 

21.5 

2.521 

1.6 

0.014 

5.6 

0.171 

9.6 

0.503 

13.6 

1.009 

17.6 

1.689 

21.6 

2.545 

1.7 

0.016 

5.7 

0.177 

9.7 

0.513 

13.7 

1.024 

17.7 

1.709 

21.7 

2.568 

1.8 

0.018 

5.8 

0.184 

9.8 

0.524 

13.8 

1.039 

17.8 

1.728 

21.8 

2.592 

1.9 

0.020 

5.9 

0.190 

9.9 

0.535 

13.9 

1.054 

17.9 

1.748 

21.9 

2.616 

2.0 

0.022 

6.0 

0.196 

10.0 

0.545 

14.0 

1.069 

18.0 

1.767 

22.0 

2.640 

2.1 

0.024 

6.1 

0.203 

10.1 

0.556 

14.1 

1.084 

18.1 

1.787 

22.1 

2.664 

2.2 

0.026 

6.2 

0.210 

10.2 

0.568 

14.2 

1.100 

18.2 

1.807 

22.2 

2.688 

2.3 

0.029 

6.3 

0.216 

10.3 

0.579 

14.3 

1.115 

18.3 

1.827 

22.3 

2.712 

2.4 

0.031 

6.4 

0.223 

10.4 

0.590 

14.4 

1.131 

18.4 

1.847 

22.4 

2.737 

2.5 

0.034 

6.5 

0.230 

10.5 

0.601 

14.5 

1.147 

18.5 

1.867 

22.5 

2.761 

2.6 

0.037 

6.6 

0.238 

10.6 

0.613 

14.6 

1.163 

18.6 

1.887 

22.6 

2.786 

2.7 

0.040 

6.7 

0.245 

10.7 

0.625 

14.7 

1.179 

18.7 

1.907 

22.7 

2.810 

2.8 

0.043 

6.8 

0.252 

10.8 

0.636 

14.8 

1.195 

18.8 

1.928 

22.8 

2.835 

2.9 

0.046 

6.9 

0.260 

10.9 

0.648 

14.9 

1.211 

18.9 

1.948 

22.9 

2.860 

3.0 

0.049 

7.0 

0.267 

11.0 

0.660 

15.0 

1.227 

19.0 

1.969 

23.0 

2.885 

3.1 

0.052 

7.1 

0.275 

11.1 

0.672 

15.1 

1.244 

19.1 

1.990 

23.1 

2.910 

3.2 

0.056 

7.2 

0.283 

11.2 

0.684 

1    15.2 

1.260 

19.2 

2.011 

23.2 

2.936 

3.3 

0.059 

7.3 

0.291 

11.3 

0.697 

15.3 

1.277 

19.3 

2.032 

23.3 

2.961 

3.4 

0.063 

7.4 

0.299 

11.4 

0.709 

15.4 

1.294 

19.4 

2.053 

23.4 

.  2.986 

3.5 

0.067 

7.5 

0.307 

11.5 

0.721 

15.5 

1.310 

19.5 

2.074 

23.5 

3.012 

3.6 

0.071 

7.6 

0.315 

11.6 

0.734 

15.6 

1.327 

19.6 

2.095 

23.6 

3.038 

3.7 

0.075 

7.7 

0.323 

11.7 

0.747 

15.7 

1.344 

19.7 

2.117 

23.7 

3.064 

3.8 

0.079 

7.8 

0.332 

11.8 

0.760 

15.8 

1.362 

19.8 

2.138 

23.8 

3.089 

3.9 

0.083 

7.9 

0.340 

11.9 

0.772 

15.9 

1.379 

19.9 

2.160 

23.9 

3.115 

4.0 

0.087 

8.0 

0.349 

12.0 

0.785 

16.0 

1.396 

20.0 

2.182 

24.0 

3.142 

4.1 

0.092 

8.1 

0.358 

12.1 

0.799 

16.1 

1.414 

20.1 

2.204 

24.1 

3.168 

4.2 

0.096 

8.2 

0.367 

12.2 

0.812 

16.2 

1.431 

20.2 

2.226 

24.2 

3.194 

4.3 

0.101 

8.3 

0.376 

12.3 

0.825 

16.3 

1.449 

20.3 

2.248 

'   24.3 

3.221 

4.4 

0.106 

8.4 

0.385 

12.4 

0.839 

16.4 

1.467 

20.4 

2.270 

24.4 

3.247 

4.5 

0.111 

8.5 

0.394 

12.5 

0.852 

16.5 

1.485 

20.5 

2.292 

24.5 

3.275 

4.6 

0.115 

8.6 

0.403 

12.6 

0.866 

16.6 

1.503 

20.6 

2.315 

24.6 

3.301 

4.7 

0.121 

8.7 

0.413 

12.7 

0.880 

16.7 

1.521 

20.7 

2.337 

24.7 

3.328 

4.8 

0.126 

8.8 

0.422 

12.8 

0.894 

16.8 

1.539 

20.8 

2.360 

24.8 

3.335 

4.9 

0.131 

8.9 

0.432 

12.9 

0.908 

16.9 

1.558 

20.9 

1 

2.383 

24.9 

1 

3.382 

104 


APPENDIX 


TABLE    III— Continued 


Diam- 
eter, 
Inches 


Area, 

Square 

Feet 


25.0 
25.1 
25.2 
25.3 
25.4 
25.5 
25.6 
25.7 
25 . 8 
25.9 

26.0 
26.1 
26.2 
26.3 


3.409 
3.436 
3.464 
3.491 
3.519 
3.547 
3.574 
3.602 
3.631 
3.659 


3.687 
3.715 
3.744 
3.773 


Diam- 

Area, 

eter, 

Square 

Inches 

Feet 

26.4 

3.801 

26.5 

3.830 

26.6 

3.860 

26.7 

3.888 

26.8 

3.917 

1   26. 9 

3.947 

27.0 

3.976 

27.1 

4.006 

27.2 

4.035 

27.3 

4.065 

27.4 

4.095 

27.5 

4.125 

27.6 

4.155 

27.7 

1 

4^  IS.. 

Diam- 
eter, 
Inches 


27.8 
27.9 

28.0 
28.1 
28.2 
28.3 
28.4 
28.5 
28.6 
28.7 
28.8 
28.9 

29.0 


Area, 

Square 

Feet 


I 
4.215 
4.246 

4.276 
4 .  307 
4.337 
4.368 
4.399 
4.430 
4.461 
4.493 
4.524 
4.555 

4.587 


Diam- 

Area, 

eter, 

Square 

Inches 

Feet 

29.1 

4.619 

29.2 

4.650 

29.3 

4 .  682 

29.4 

4.714 

29.5 

4 .  746 

29.6 

4.779 

29.7 

4.811 

29.8 

4.844 

29.9 

4.876 

30.0 

4.909 

31.0 

5.241 

32.0 

5.585 

33.0 

5.940 

34.0 

i 

6 .  305 

Diam- 
eter, 
Inches 


Area, 

Square 

Feet 


35 . 0 
36.0 
37.0 
38.0 
39.0 

40.0 
41.0 
42.0 
43.0 
44.0 

45.0 
46.0 
47.0 


6.681 
7.069 
7.467 

7.876 
8 .  296 

8.727 
9.168 
9.621 
10.085 
10.559 

11.045 
11.541 
12.048 


Diam- 

Area, 

eter, 

Square 

Inches 

Feet 

48.0 

12.566 

49.0 

13.095 

50.0 

13.635 

51.0 

14.186 

52.0 

14.748 

53.0 

15.321 

54.0 

15.904 

55.0 

16.499 

56.0 

17.104 

57.0 

17.721 

58.0 

18.348 

59.0 

18.986 

TABLES 


105 


TABLE    IV 

Volumes  of  Frustums  of  Coxes.   Scaled   with  Scribxer   Rule  in   16-foot   Logs   Down 

TO  8-INCH  Tops 


Height  in  Number  of  Logs 


D.B.H.j   U 

2 

3 

4 

5 

6 

7 

8 

9 

10 

10     43 

74 

115 

159 

11     44 

80 

128 

175 

12     46 

86 

137 

192 

13     47 

91 

150 

212 

271 

14     48 

96 

165 

232 

300 

15     50 

103 

179 

257 

331 

405 

16     52 

111 

195 

279 

366 

449 

528 

17     54 

120 

210 

311 

406 

496 

598 

684 

18     56 

129 

231 

338 

438 

548 

650 

756 

855 

968 

19 

137 

253 

363 

485 

591 

707 

822 

938 

1065 

20 

146 

270 

395 

530 

651 

780 

908 

1030 

1165 

21 

160 

291 

435 

572 

710 

828 

982 

1126 

1278 

22 

174 

317 

472 

618 

775 

931 

1095 

1227 

1391 

23 

182 

342 

510 

675 

843 

998 

1155 

1329 

1507 

24 

191 

364 

550 

720 

895 

1097 

1265 

1439 

1725 

25 

204 

391 

584 

772 

972 

1182 

1346 

1532 

1760 

26 

217 

426 

624 

836 

1052 

1250 

1458 

1669 

1886 

27 

231 

449 

666 

901 

1105 

1337 

1566 

1804 

2038 

28 

245 

476 

719 

954 

1194 

1441 

1699 

1916 

2199 

29 

259 

508 

755 

1026 

1285 

1552 

1848 

2062 

2337 

30 

272 

539 

809 

1092 

1363 

1639 

1908 

2208 

2482 

31 

292 

569 

868 

1160 

1446 

1732 

2019 

2324 

2626 

32 

312 

595 

926 

1233 

1536 

1837 

2161 

2451 

2802 

33 

324 

636 

982 

1299 

1608 

1930 

2274 

2582 

2965 

34 

336 

682 

1029 

1355 

1704 

2059 

2410 

2772 

3103 

35 

351 

717 

1072 

1424 

1808 

2128 

2527 

2897 

3262 

36 

366 

754 

1117 

1509 

1896 

2272 

2654 

3041 

3433 

37 

388 

792 

1180 

1587 

1987 

2374 

2773 

3171 

3591 

38 

409 

827 

1243 

1662 

2085 

2473 

2920 

3340 

3773 

39 

422 

851 

1296 

1745 

2127 

2613 

3063 

3493 

3954 

40 

436 

887 

1331 

1805 

2236 

2743 

3195 

3683 

4164 

41 

464 

929 

1401 

1878 

2366 

2874 

3375 

3864 

4395 

42   1   ... 

491 

973 

1455 

1940 

2501 

3037 

3515 

4030 

4545 

43   1   ... 

511 

1018 

1506 

2040 

2637 

3153 

3647 

4214 

4739 

44 

532 

1048 

1593 

2174 

2730 

3243 

3846 

4399 

5000 

45 

1 

'•    1084 

1 

1658 

2269 

2838 

3384 

4011 

4629 

5202 

106 


APPENDIX 


TABLE    V  ' 
VOLUMK   Tahle— Douglas   Fi„,    ,n    Fekt,   B.M.,   Based   on    D.B.H.    and   30-foot   Height 

Classes 


D.B.H. 

to  75 

76  to  105 

106  to  135 

136  to  165 

166  to  195 

196  to  225 

220  to  255 

256  Up 

10 

80 

100 

130 

160 

12 

100 

140 

190 

240 

310 

14 

140 

200 

250 

330 

430 

540 

IG 

190 

220 

320 

440 

540 

690 

18 

240 

320 

410 

550 

680 

840 

980 

20 

290 

380 

480 

680 

850 

1,010 

1,170 

22 

350 

460 

580 

810 

980 

1,190 

1,360 

24 

430 

550 

700 

910 

1,150 

1,390 

1,580 

26 

510 

640 

810 

1000 

1,340 

1,600 

1,820 

28 

590 

750 

930 

1250 

1,550 

1,820 

2,080 

30 

680 

860 

1080 

1440 

1,770 

2,080 

2,310 

32 

780 

980 

1230 

1620 

2,020 

2,300 

2,610 

34 

890 

1100 

1400 

1830 

2,280 

2,590 

2,930 

36 

1000 

1240 

1570 

2040 

2,550 

2,700 

3,270 

3,630 

38 

1400 

1760 

2260 

2,850 

3,230 

3,030 

4,020 

40 

1560 

1980 

2510 

3,170 

3,600 

4,030 

4,410 

42 

1740 

2190 

2720 

3,510 

3,970 

4,040 

4,870 

44 



1910 

2420 

2950 

3,810 

4,300 

4,870 

5,390 

46 



2660 

3360 

4,180 

4,770 

5,200 

5,870 

48 

2920 

3690 

4,570 

5,200 

5,730 

6,330 

50 

3190 

4030 

4,950 

5,650 

6,200 

6,860 

52 

3480 

4400 

5,400 

6,090 

6,680 

7,470 

54 



4800 

5,900 

6,140 

7,210 

8,070 

56 

.... 

5200 

6,350 

7,070 

7,760 

8,660 

58 

5620 

6,800 

7,000 

8,320 

9,330 

60 

6150 

7,260 

8,150 

8,910 

10,010 

62 

6420 

7,710 

8,650 

9,570 

10,740 

64 

6790 

8,280 

9,220 

10,200 

11,590 

66 

7150 

8,730 

9,870 

10,900 

12,470 

68 

7470 

9,240 

10,510 

11,770 

13,330 

70 

7790 

9,870 

11,200 

12,540 

14,250 

72 



10,260 

11,880 

13,320 

15,240 

74 

10,670 

12,600 

14,190 

16,160 

76 



11,050 

13,440 

15,050 

17,190 

78 

11,410 

14,140 

15,840 

17,850 

80 

11,760 

14,850 

16,080 

18,540 

82 





15,480 

17,400 

19,230 

84 

16,030 

18,010 

19,980 

86 

16,510 

18,550 

20,640 

88 

10,930 

19,040 

21,240 

90 

17,370 

19,500 

21,810 

92 

19,920 

22,340 

94 

20,300 

22,810 

96 

20,080 

23,210 

98 

::::  j 

21,020 

23,610 

100 

.... 



21,360 

23,970 

Note.— Tables  V,  VI,  VII,  VIII  are  based  upon  data  collected  in  the  lower  slope,  Douglas 
fir-cedar  type  of  King  and  Snohomish  Counties  in  Western  Washington.  The  trees  were 
scaled  by  the  Scribner  Decimal  C  Rule  to  a  point  8  inches  in  diameter  at  the  tops  inside  the 
bark.  The  Douglas  fir  table  is  based  upon  the  measurement  of  about  600  trees  and  the  other 
tables  each  are  based  upon  the  measurement  of  about  300  trees. 


TABLES 


107 


TABLE   VI 
Volume  Table — Westekn   Red   Cedar — in  Feet   B.M.   Based   on   D.B.H.    and   30-foot 

Height  Classes 


D.B.H. 

to  75 

re  to  105 

L06tol35  136  to  165 

166  to  195 

1         1 
196  to  225  226  to  255 

256  Up 

12 

90 

102 

14 

120 

192 

210 

16 

158 

209 

265 

18 

196 

256 

322 

20 

235 

302 

386 

510 

570 

22 

275 

352 

456 

590 

710 

24 

406 

528 

700 

875 

26 

460 

598 

818 

1.045 

28 

557 

670 

910 

1,200 

30 

629 

749 

1016 

1,360 

32 

836 

1145 

1,560 

34 

940 

1303 

1,780 

36 

1122 

1498 

1,990 

38 

1272 

1718 

2,200 

40 

1700 

1945 

2,425 

2,650 

2,875 

42 

1855 

2178 

2,670 

2,875 

3,080 

44 

.... 

2015 

2412 

2,915 

3,165 

3,415 

46 

2180 

2768 

3,175 

3,475 

3,775 

48 

2340 

2940 

3,435 

3,800 

4,165 

50 

2500 

3480 

3,690 

4,090 

4,490 

52 

2670 

3500 

3,9.50 

4,425 

4,900 

54 

.... 

2840 

3740 

4,225 

4,750 

5,275 

56 

3010 

3815 

4,500 

5,100 

5,700 

58 

3190 

4160 

4,800 

5,470 

6,140 

60 

3375 

4390 

5,105 

5,825 

6,545 

62 

3555 

4615 

5,410 

6,200 

6,990 

64 

3750 

4850 

5,725 

6,560 

7,395 

66 

.... 

3925 

5075 

6,030 

6,920 

7,810 

68 

.... 

4100 

5300 

6,340 

7,280 

8,220 

70 

4280 

5520 

6,640 

7,600 

8,560 

72 

4470 

5750 

6,935 

7,950 

8,965 

74 

.... 

.... 

4650 

5970 

7,220 

8,275 

9,330 

76 

4825 

6190 

7,505 

8,600 

9,695 

78 

5010 

6425 

7,795 

8,925 

10,055 

80 

5200 

6670 

8,080 

9,2.50 

10,420 

82 

.... 

i  '.'.'.'. 

.... 

6925 

8,400 

9,.575 

10,750 

84 

.... 

7200 

8,700 

9,975 

11,250 

86 

7475 

9,000 

10,350 

11,700 

88 

7750 

9,300 

:   10,750 

12,200 

90 

.... 

8000 

9,600 

11,200 

12,800 

92 

8265 

9,940 

11,575 

13,210 

94 

8550 

10,265 

11,980 

13,695 

96 

88.50 

10,600 

12,350 

14,100 

98 

9125 

1  10,900 

12,675 

14,450 

100 

j   .... 

9400 

;  11,200 

13,000 

i  14,800 

108 


APPENDIX 


Volume  Table — Silver  Fir- 


TABLE    VII 
-IN  Feet,  B.M.,  Based  on  D.B.H.  and  30-foot  Height  Classes 


D.B.H. 

To  75 

76  to  105 

100  to  135 

136  to  165 

166  to  195 

196  Up 

10 

60 

65 

75 

12 

95 

110 

135 

' 

14 

140 

160 

250 

16 

190 

240 

360 

500 

18 

240 

315 

470 

610 

20 

310 

405 

580 

770 

1,190 

22 

380 

510 

700 

920 

1,360 

24 

480 

620 

840 

1,110 

1,540 

26 

590 

740 

950 

1,290 

1,730 

28 

700 

870 

1100 

1,470 

1,920 

30 

820 

1020 

1270 

1,660 

2,140 

2,660 

32 

930 

1170 

1450 

1,870 

2,370 

2,900 

34 

1090 

1380 

1650 

2,100 

2,620 

3,170 

36 

1240 

1530 

1860 

2,360 

2,900 

3,450 

38 

1390 

1720 

2090 

2,650 

3,190 

3,760 

40 

1560 

1930 

2330 

2,880 

3,490 

4,080 

42 

1730 

2160 

2590 

3,200 

3,840 

4,440 

44 

1900 

2400 

2880 

3,500 

4,180 

4,750 

46 

2080 

2640 

3170 

3,790 

4,.520 

5,090 

48 

2260 

2890 

3480 

4,110 

4,860 

5,440 

50 

2450 

3150 

3790 

4,410 

5,200 

5,780 

52 

2630 

3420 

4100 

4,730 

5,.540 

6,140 

54 

3670 

4430 

5,080 

5,580 

6,500 

56 

3950 

4750 

5,460 

6,240 

6,850 

58 

4220 

5090 

5,820 

6,570 

7,230 

60 

4500 

5450 

■  6,200 

6,940 

7,620 

62 

4770 

5800 

6,570 

7,290 

8,020 

64 

6150 

6,960 

7,670 

8,440 

66 

6510 

7,340 

8,000 

8,970 

68 

6880 

7,710 

8,460 

9,310 

70 

.... 

7250 

8,110 

8,850 

9,750 

72 

.... 

7610 

8,.500 

9,260 

10,200 

74 

8,870 

9,650 

10,630 

76 

9,230 

10,030 

11,030 

78 

9,570 

10,380 

11,380 

80 

9,900 

10,700 

11,750 

82 

10,200 

11,010 

12,080 

84 

10,470 

11,320 

12,380 

86 

11,600 

12,600 

88 

.... 

11,860 

12,920 

90 

12,100 

13,150 

92 

12,330 

13,380 

94 

13,000 

96 

13,820 

98 
100 

14,020 
14,220 

TABLES 


109 


TABLE    VIII 
Volume   Table — Western    Hemlock — in    Feet,    B.M., 

Height  Classes 


Based    ox     D.B.H.    and     30-fc)ot 


To  75 


50 
80 
130 
200 
260 
350 
430 
510 
590 


76  to  105   106  to  135 


60 
100 
150 
220 
280 
370 
460 
550 
650 
760 

900 
1050 
1200 
1390 


80 
140 
220 
300 
390 
490 
580 
700 
830 
980 

1140 
1300 
1500 
1710 
1940 
2190 
2480 
2800 
3150 
3550 

3950 
4430 
4860 
5260 


136  to  165 


480 

590 

710 

850 

1000 

1170 

1360 

1560 
1780 
2040 
2300 
2650 
2850 
3200 
3600 
4080 
4580 

5070 
5480 
5840 
6170 
6460 
6750 
7020 
7260 
7460 
7640 

7820 


166  to  195 


1200 
1380 
1600 
1840 

2100 
2350 
2750 
3150 
3560 
3980 
4410 
4850 
5300 
5700 

6120 
6450 
6750 
7030 
7270 
7500 
7710 
7920 
8110 
8290 

8450 
8610 
8770 
8920 
9060 
9180 
9290 
9400 
9500 
9580 

9670 


196  Up 


2,710 
3,050 
3,460 
3,910 
4,420 
4,920 
5,400 
5,840 
6,220 
6,570 

6,890 
7,180 
7,260 
7,640 
7,860 
8,060 
8,270 
8,440 
8,620 
8,790 

8,950 
9,100 
9,230 
9,360 
9,480 
9,570 
9,660 
9,740 
9,820 
9,900 

9.970 
10,030 
10.100 
10,160 
10,210 
10.270 


110 


APPENDIX 


TABLE   IX 
ScRiBNER  Decimal  "C"  Log  Rule  for  Logs  6  to  32  Feet  in  Length 


Length- 

-Feet 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

Contents, 

Board  Feet 

m  Tens 

0.5 

0.5 

1 

1 

1 

2 

2 

2 

3 

3 

3 

4 

4 

5 

0.5 

1 

1 

2 

2 

3 

3 

3 

4 

4 

4 

5 

5 

6 

1 

1 

2 

2 

2 

3 

3 

3 

4 

4 

5 

6 

6 

7 

1 

2 

3 

3 

3 

4 

4 

4 

5 

6 

6 

7 

8 

9 

2 

3 

3 

3 

4 

6 

6 

7 

8 

9 

9 

10 

11 

12 

2 

3 

4 

4 

5 

7 

8 

8 

9 

10 

11 

12 

13 

14 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

4 

5 

6 

7 

8 

10 

11 

12 

13 

15 

16 

17 

18 

19 

4 

6 

7 

9 

10 

11 

13 

14 

16 

17 

19 

20 

21 

23 

5 

7 

9 

11 

12 

14 

16 

18 

20 

21 

23 

25 

27 

28 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

7 

9 

12 

14 

16 

18 

21 

23 

25 

28 

30 

32 

35 

37 

8 

11 

13 

16 

19 

21 

24 

27 

29 

32 

35 

37 

40 

43 

9 

12 

15 

18 

21 

24 

27 

30 

33 

36 

39 

42 

45 

48 

11 

14 

17 

21 

24 

28 

31 

35 

38 

42 

45 

49 

52 

56 

12 

15 

19 

23 

27 

30 

34 

38 

42 

46 

49 

53 

57 

61 

13 

17 

21 

25 

29 

33 

38 

42 

46 

50 

54 

58 

63 

67 

14 

19 

23 

28 

33 

38 

42 

47 

52 

57 

61 

66 

71 

75 

15 

21 

25 

30 

35 

40 

45 

50 

55 

61 

66 

71 

76 

81 

17 

23 

29 

34 

40 

46 

52 

57 

63 

69 

75 

80 

86 

92 

19 

25 

31 

37 

44 

50 

56 

62 

69 

75 

82 

88 

94 

100 

21 

27 

34 

41 

48 

55 

62 

68 

75 

82 

89 

96 

103 

110 

22 

29 

36 

44 

51 

58 

65 

73 

80 

87 

95 

102 

109 

116 

23 

31 

38 

46 

53 

61 

68 

76 

84 

91 

99 

107 

114 

122 

25 

33 

41 

49 

57 

66 

74 

82 

90 

99 

107 

115 

123 

131 

27 

36 

44 

53 

62 

71 

80 

89 

98 

106 

115 

124 

133 

142 

28 

37 

46 

55 

64 

74 

83 

92 

101 

110 

120 

129 

138 

147 

29 

39 

49 

59 

69 

78 

88 

98 

108 

118 

127 

137 

147 

157 

30 

40 

50 

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

160 

33 

44 

55 

66 

77 

88 

98 

109 

120 

131 

142 

153 

164 

175 

35 

46 

58 

69 

81 

92 

104 

115 

127 

138 

150 

161 

173 

185 

39 

51 

64 

77 

90 

103 

116 

129 

142 

154 

167 

180 

193 

206 

40 

54 

67 

80 

93 

107 

120 

133 

147 

160 

174 

187 

200 

214 

42 

56 

70 

84 

98 

112 

126 

140 

154 

168 

182 

196 

210 

224 

45 

60 

75 

90 

105 

120 

135 

150 

166 

181 

196 

211 

226 

241 

48 

64 

79 

95 

111 

127 

143 

159 

175 

191 

207 

223 

238 

254 

50 

67 

84 

101 

117 

134 

151 

168 

185 

201 

218 

235 

252 

269 

52 

70 

87 

105 

122 

140 

157 

174 

192 

209 

227 

244 

2^9 

279 

56 

74 

93 

111 

129 

148 

166 

185 

204 

222 

241 

259 

278 

296 

57 

76 

95 

114 

133 

152 

171 

190 

209 

228 

247 

266 

286 

304 

59 

79 

99 

119 

139 

159 

178 

198 

218 

238 

258 

278 

297 

317 

62 

83 

104 

124 

145 

160 

186 

207 

228 

248 

269 

290 

310 

331 

65 

86 

108 

130 

151 

173 

194 

216 

238 

260 

2S1 

302 

324 

346 

67 

90 

112 

135 

157 

180 

202 

225 

247 

270 

292 

314 

337 

359 

70 

94 

117 

140 

164 

187 

211 

234 

257 

281 

304 

328 

351 

374 

73 

97 

122 

146 

170 

195 

219 

243 

268 

292 

315 

341 

365 

389 

76 

101 

127 

152 

177 

202 

228 

253 

278 

304 

329 

354 

380 

405 

79 

105 

132 

158 

184 

210 

237 

263 

289 

316 

341 

368 

395 

421 

82 

109 

137 

164 

191 

218 

246 

273 

300 

328 

355 

382 

410 

437 

85 

113 

142 

170 

198 

227 

255 

283 

312 

340 

368 

397 

425 

453 

88 

118 

147 

176 

206 

235 

264 

294 

323 

353 

382 

411 

441 

470 

91 

122 

152 

183 

213 

244 

274 

304 

335 

365 

396 

426 

457 

487 

95 

126 

158 

189 

221 

252 

284 

315 

347 

379 

410 

442 

473 

505 

98 

131 

163 

196 

229 

261 

294 

327 

359 

392 

425 

457 

490 

523 

101 

135 

109 

203 

237 

270 

304 

338 

372 

400 

439 

473 

507 

541 

TABLES 


111 


TABLE    lX~Continued 


Length 

—Feet 

Diam- 

eter, 
Inches 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

2S 

30 

32 

Contents 

Board  Feet 

in  Tens 

61 

105 

140 

175 

210 

245 

280 

315 

350 

385 

420 

455 

490 

525 

560 

62 

108 

145 

181 

217 

253 

289 

325 

362 

398 

434 

470 

506 

542 

679 

63 

112 

149 

187 

224 

261 

299 

336 

373 

411 

448 

485 

523 

560 

597 

64 

116 

154 

193 

232 

270 

309 

348 

387 

425 

464 

503 

541 

580 

619 

65 

119 

159 

199 

239 

279 

319 

358 

398 

438 

478 

518 

558 

597 

637 

66 

123 

164 

206 

247 

288 

329 

370 

412 

453 

494 

535 

576 

617 

659 

67 

127 

170 

212 

254 

297 

339 

381 

423 

466 

508 

550 

593 

635 

677 

68 

131 

175 

219 

262 

306 

350 

393 

437 

480 

524 

568 

611 

655 

699 

69 

135 

180 

226 

271 

316 

361 

406 

452 

497 

542 

587 

632 

677 

723 

70 

139 

186 

232 

279 

325 

372 

419 

465 

512 

558 

605 

651 

698 

744 

71 

144 

192 

240 

287 

335 

383 

430 

478 

526 

574 

622 

670 

717 

765 

72 

148 

197 

247 

296 

345 

395 

444 

493 

543 

592 

641 

691 

740 

789 

73 

152 

203 

254 

305 

356 

406 

457 

508 

559 

610 

661 

712 

762 

813 

74 

157 

209 

261 

314 

366 

418 

471 

523 

576 

628 

680 

733 

785 

837 

75 

161 

215 

269 

323 

377 

430 

484 

538 

592 

646 

700 

754 

807 

861 

76 

166 

221 

277 

332 

387 

443 

498 

553 

609 

664 

719 

775 

830 

885 

77 

171 

228 

285 

341 

398 

455 

511 

568 

625 

682 

739 

796 

852 

909 

78 

176 

234 

293 

351 

410 

468 

527 

585 

644 

702 

761 

819 

878 

936 

79 

180 

240 

301 

361 

421 

481 

541 

602 

662 

722 

782 

842 

902 

963 

80 

185 

247 

309 

371 

432 

494 

550 

618 

680 

742 

804 

866 

927 

989 

81 

190 

254 

317 

381 

444 

508 

572 

635 

699 

762 

826 

889 

953 

1016 

82 

196 

261 

326 

391 

456 

521 

586 

652 

717 

782 

847 

912 

977 

1043 

83 

201 

268 

335 

401 

468 

535 

601 

668 

735 

802 

869 

936 

1002 

1069 

84 

206 

275 

343 

412 

481 

549 

618 

687 

755 

824 

893 

961 

1030 

1099 

85 

210 

281 

351 

421 

491 

561 

631 

702 

772 

842 

912 

982 

1052 

1123 

86 

215 

287 

359 

431 

503 

575 

646 

718 

790 

862 

934 

1006 

1077 

1149 

87 

221 

295 

368 

442 

516 

589 

663 

737 

810 

884 

958 

1031 

1105 

1179 

88 

226 

301 

377 

452 

527 

603 

678 

753 

829 

904 

979 

1055 

1130 

1205 

89 

231 

308 

385 

462 

539 

616 

693 

770 

847 

924 

1001 

1078 

1155 

1232 

90 

236 

315 

393 

472 

551 

629 

708 

787 

865 

944 

1023 

1101 

1180 

1259 

91 

241 

322 

402 

483 

563 

644 

725 

805 

886 

966 

1047 

1127 

1208 

1288 

92 

246 

329 

411 

493 

575 

657 

739 

822 

904 

986 

1068 

1150 

1232 

1315 

93 

251 

335 

419 

503 

587 

671 

754 

838 

922 

1006 

1090 

1174 

1257 

1341 

94 

257 

343 

428 

514 

600 

685 

771 

857 

942 

1028 

1114 

1199 

1285 

1371 

95 

262 

350 

437 

525 

612 

700 

788 

875 

963 

1050 

1138 

1225 

1313 

1400 

96 

268 

357 

446 

536 

625 

715 

804 

893 

983 

1072 

1161 

1251 

1340 

1429 

97 

273 

364 

455 

546 

637 

728 

819 

910 

1001 

1092 

1183 

1274 

1365 

1456 

98 

278 

371 

464 

557 

650 

743 

835 

928 

1021 

1114 

1207 

1300 

1392 

1485 

99 

284 

379 

473 

568 

663 

757 

852 

947 

1041 

1136 

1231 

1325 

1420 

1515 

100 

289 

386 

482 

579 

675 

772 

869 

965 

1062 

1158 

1255 

1351 

1448 

1544 

101 

295 

393 

492 

590 

688 

787 

885 

983 

1082 

1180 

1278 

1377 

1475 

1573 

102 

301 

401 

502 

602 

702 

803 

903 

1003 

1104 

1204 

1304 

1405 

1505 

1605 

103 

307 

409 

512 

614 

716 

819 

921 

1023 

1126 

1228 

1330 

1433 

1535 

1637 

104 

313 

417 

522 

626 

730 

835 

939 

1043 

1148 

1252 

1356 

1461 

1565 

1669 

105 

319 

425 

532 

638 

744 

851 

957 

1063 

1170 

1276 

1382 

1489 

1595 

1701 

106 

325 

433 

542 

650 

758 

867 

975 

1083 

1192 

1300 

1408 

1517 

1625 

1733 

107 

331 

442 

553 

663 

773 

884 

995 

1105 

1216 

1326 

1437 

1547 

16.58 

1768 

lOS 

337 

450 

563 

675 

788 

900 

1013 

1125 

1238 

1350 

1463 

1575 

1688 

1800 

109 

344 

459 

573 

688 

803 

917 

1032 

1147 

1261 

1376 

1491 

1605 

1720 

1835 

110 

350 

467 

583 

700 

817 

933 

1050 

1167 

1283 

1400 

1517 

1633 

1750 

1867 

111 

356 

475 

594 

713 

832 

951 

1069 

1188 

1307 

U26 

1545 

1664 

1782 

1901 

112 

362 

483 

604 

725 

846 

967 

1087 

1208 

1329 

1450 

1571 

1692 

1812 

1933 

113 

369 

492 

615 

738 

861 

984 

1107 

1230 

1353 

1476 

1599 

1722 

1845 

1968 

114 

375 

501 

626 

751 

876 

1001 

1126 

1252 

1377 

1502 

1627 

1752 

1877 

2003 

115 

382 

509 

637 

764 

891 

1019 

1146 

1273 

1401 

1528 

1655 

1783 

1910 

2037 

116 

389 

519 

648 

778 

908 

1037 

1167 

1297 

1426 

1556 

1686 

1815 

1945 

2075 

117 

396 

528 

660 

792 

924 

1056 

1188 

1320 

1452 

1584 

1716 

1848 

1980 

2112 

118 

403 

537 

672 

806 

940 

1075 

1209 

1343 

1478 

1612 

1746 

1881 

2015 

2149 

119 

410 

547 

683 

820 

957 

1093 

1230 

1367 

1503 

1640 

1777 

1913 

2050 

2187 

120 

417 

556 

695 

834 

973 

1112 

1251 

1390 

1529 

1668 

1807 

1946 

2085 

2224 

112 


APPENDIX 


TABLE  X* 

[ELD  FOR  Even-aged  Stands  of  Douglas  Fir  on  Quality  1  Soils,  Based  on  Two-site 
Qualities  for  the  Type,  Namely,  Western  Foothills  of  the  Cascade  Mountains 
IN  Washington  and  Oregon.     (Read  from  Curves.) 


Average 

Average 

No.  of 

Total 

Diameter 
of 

Height 
of 

Yield 

Annual 
Growth 

Yield 

Annual 
Growth 

Age 

Trees 
per  Acre 

Basal 
Area 

Average 
Tree 

Average 
Tree 

per 
Acre 

per  Acre 
in  Each 
Decade 

per 
Acre 

per  Acre 
in  Each 
Decade 

Years 

Sq.  Ft. 

Inches 

Feet 

Cu.  Ft. 

Cu.  Ft. 

Ft.  B.M. 

Ft.  B.M. 

10 



1,000 

20 

990 

116 

4.6 

32.0 

2,150 

115 

30 

580 

149 

6.9 

46.0 

3,550 

140 

40 

410 

177 

8.9 

59 . 0 

5,400 

185 

12,400 

50 

340 

199 

10.4 

69.5 

7,550 

215 

28,000 

1560 

60 

265 

218 

12.3 

82.0 

9,650 

210 

41,000 

1300 

70 

208 

234 

14.4 

95.0 

11,500 

185 

51,700 

1070 

80 

107 

247 

16.5 

107 . 5 

13,100 

160 

61,100 

940 

90 

137 

261 

18.7 

120 . 5 

14,400 

130 

70,300 

920 

100 

115 

275 

20.9 

134.5 

15,000 

120 

79,800 

950 

110 

100 

288 

23.0 

147.0 

16,750 

115 

90,300 

1050 

120 

92 

301 

24.5 

156.5 

17,800 

105 

101,500 

1120 

130 

90 

312 

25.2 

161 . 0 

18,850 

105 

113,000 

1150 

140 

88 

323 

25.9 

166.0 

19,900 

105 

122,000 

960 

Based  on  252^  acres  (361  sample  plots). 

Note. — Including  only  Douglas  fir,  western  hemlock,  grand  fir,  and  Sitka  s^iruce;  over 
95  per  cent  of  the  trees  are  Douglas  fir. 

The  yield  in  cubic  feet  includes  the  contents  of  the  whole  stem  of  all  the  trees;  that  iu 
board  feet  includes  only  the  merchantable  contents  of  trees  12  inches  and  more  in  dianictor 
at  breast  height,  taken  to  a  top  diameter  of  8  inches  inside  the  bark. 

*From    Cir.     No.    175,    Forest   Service,    U.    S.     Dept.     Agr.,     Growth    and    Managoinent   of 
Douglas  Fir  in  the  Pacific  Northwest,  by  T.  T.  Munger. 


DATA  SERIES 


113 


DATA  SERIES 

DATA   SERIES    I 

DouGL.\s  Fir  Stem  Measurements 

Collected  in  the  West  Coast  Lower  Slope  Type  of  Washington  and  Oregon 


D.B.H. 

Total 
Height 

Mer. 
Length  to 
8  inches 

No.  of 
16.2-foot 
Sections  to 
8  Inches 

Volume, 
B.M., 

16.2-foot 
Sections  to 
S Inches 

Volume, 
Cubic  Feet 

(stem) 

Used 
Length 

Volume, 
B.M.  (as 
cut  into 
logs  by 
logger) 

31.1 

180.6 

140.0 

81 

1401 

255.5 

120.3 

27.1 
25.0 

141.2 
129.2 

116.6 
97.6 

7i 
6 

1046 
710 

185.3 
130.0 

67.0 
71.9 

24.5 

119.8 

92.1 

ol 

730 

144.3 

70.6 

22.2 
24.2 
27.0 

159.1 
148.7 
130.2 

117.5 
114.1 
115.6 

7k 
7z 
7i 

590 

890 

1000 

120.2 
172.1 
174.4 

97.6 

96.2 

105.5 

31.0 
24.2 

179.7 
150.3 

151.1 
96.1 

9§ 
6 

1550 
540 

253.1 
120.4 

79.5 

78.6 

13.8 

139 . 8 

86.0 

5^ 

204 

53.2 

80.0 

31.2 
27.0 
17.0 
23.5 
26.0 
27.0 
32.5 

178.1 
158.1 
115.6 
161.4 
153.7 
158.1 
184.2 

85.6 

139 . 8 
121.1 

126.3 

5i 

SI 
7h 

8 

1290 
1140 

314.2 
255.5 
72.5 
206.2 
202 . 3 
255.5 
271.8 

123.2 
80.6 
65.0 

127.4 
99.0 
83.6 

126.3 

1550 

1256 

336 

980 
1510 

12.5 
17.0 

113.2 
124.8 

69.6 

68.2 

4i 

4i 

160 
.   240 

40.3 
76.9 

408.8 
37.1 

140 
160 

35.0 

183.0 

157.4 

91 

3620 

394.9 

112.2 

2590 

19.8 
16.7 

123.9 
127.3 

85.8 

o\ 

690 

101.4 
78.1 

81.0 
64.6 

440 
440 

26.1 

174.7 

135.3 

H 

1162 

193.7 

101.9 

1000 

32.7 

175.0 

149.4 

9i 

1720 

285.9 

131.2 

1660 

17.1 

152.1 

103.0 

6^ 

360 

86.3 

70.3 

340 

26.3 

149.3 

198.7 

105.0 

1040 

29.0 
39  5 

156.7 
222.4 

231.1 
321.5 

85.9 
135.9 

•  1180 
2650 

12   1 

115.2 

36.6 

80 

17.8 

101.8 

64.8 

4 

260 

61.0 

49.4 

190 

12.1 

97.0 

43.2 

21 

80 

23.7 

24.7 

60 

11.2 

96.3 

41.4 

2h 

70 

24.5 

36.1 

50 

18.7 

110.0 

73.5 

61.0 

330 

27.1 

160.7 

136 . 1 

8i 

182.7 

103.2 

870 

29.0 

173.2 

134.6 

8^ 

201.6 

87.6 

1860 

32.0 

166.8 

146.8 

91 

260.8 

103.9 

1430 

30.9 

199.4 

162.0 

10 

1920 

305.4 

139.4 

1990 

38.5 

225.4 

162.0 

10 

2780 

406.8 

162.0 

2710 

35.0 

254.3 

194.4 

12 

4030 

515.2 

162.0 

3840 

33.5 

226.3 

178.2 

11 

2610 

426.1 

116.2 

2180 

29.3 

197.7 

162.0 

10 

1820 

225.0 

114.1 

1560 

114 


APPENDIX 

DATA   SERIES    I— Continued 


No.  of 
16.2-foot 
Sections  to 
8  Inches 

Volume, 

Volume, 

D.B.H. 

Total 
Height 

Mer. 
Length  to 
8  Inches 

B.M., 

16.2-foot 
Sections  to 
8  Inches 

Volume, 

Cubic  Feet 

(stem) 

Used 
Length 

B.M.  (as 
cut  into 
logs  by 
logger) 

44.0 

216.6 

178.2 

11 

4210 

625.3 

133.2 

3130 

23.3 

182.5 

145.8 

9 

910 

182.6 

98.9 

890 

31.0 

200.5 

162.0 

10 

2110 

383.9 

105.7 

1660 

37.5 

214.8 

162.0 

10 

2750 

422.5 

131.1 

2460 

45.5 

215.0 

194.4 

12 

5190 

721.2 

135.1 

4870 

24.0 

168.0 

145.8 

9 

1330 

203.2 

104.6 

1100 

44.4 

266.8 

178.2 

11 

4210 

614.5 

131.4 

3560 

39.4 

196.8 

194.4 

12 

4590 

655.2 

157.8 

4380 

23.5 

201.5 

145.8 

9 

1480 

238.2 

102.3 

1080 

19.1 

190.2 

129.6 

8 

520 

122.3 

97.2 

510 

32.7 

208.3 

178.2 

11 

2390 

375.1 

102.1 

1860 

19.2 

179.5 

113.4 

7 

680 

134.2 

65.3 

470 

36.2 

199.2 

178.2 

11 

3280 

469.5 

118.2 

2650 

26.0 

184.7 

145 . 8 

9 

1260 

207.6 

106.3 

1080 

25.0 

198.3 

162.0 

10 

1610 

252.9 

145.1 

1570 

33.0 

191.0 

162.0 

10 

2310 

344.1 

130.4 

1980 

21.2 

165.5 

113.4 

7 

680 

110.6 

97.5 

500 

31.6 

222.0 

162.0 

10 

2320 

326.9 

148.0 

2290 

26.3 

146.1 

129.6 

8 

1000 

189.6 

97.5 

820 

22.9 

144.0 

129.6 

8 

780 

124.2 

72.5 

620 

13.5 

147.0 

81.0 

5 

220 

49.6 

64.9 

160 

24.4 

181.0 

129.6 

8 

910 

149.2 

129.9 

820 

24.4 

180.1 

145.8 

9 

990 

178.3 

130.0 

880 

25.0 

189.1 

145.8 

9 

1310 

188.4 

129.6 

1150 

30.5 

191.5 

178.2 

11 

2420 

381.2 

162.0 

2191 

17 . 5 

135.7 

113.4 

7 

560 

103.1 

97.7 

430 

26.5 

183.6 

129.6 

8 

1040 

188.4 

129 . 6 

860 

27.5 

181.0 

129.6 

8 

1340 

219.5 

98.0 

1240 

21.1 

134.7 

113.4 

7 

770 

140.3 

80.0 

710 

23.8 

160.0 

145.8 

0 

1120 

191.2 

102.0 

1100 

21.7 

147.0 

113.4 

7 

1040 

110.5 

104.0 

1010 

32.5 

197.3 

162.0 

10 

2640 

394.0 

149.5 

2390 

22.5 

143.3 

113.4 

7 

500 

104.4 

89.1 

370 

17.9 

114.5 

81.0 

5 

350 

91.2 

74.0 

300 

32.0 

183.3 

162.0 

10 

1890 

314.8 

140.0 

1740 

27.8 

204.2 

162.0 

10 

1630 

215.0 

125.5 

1420 

28.0 

195.0 

162.0 

10 

1910 

253.3 

119.3 

1530 

21.0 

163.0 

129.6 

8 

900 

158.1 

146.0 

780 

26.5 

181.4 

162.0 

10 

1710 

275.6 

145.2 

1670 

30.6 

194.0 

162.0 

10 

1970 

314.4 

106.5 

1916 

28.5 

191.8 

162.0 

10 

2110 

319.4 

143.1 

1660 

24.5 

176.5 

145.8 

9 

1260 

215.7 

145 . 3 

1100 

.24.5 

192.8 

162.0 

10 

1570 

252.1 

135.8 

1210 

24.5 

195 . 3 

162.0 

10 

1650 

257.7 

81.3 

1130 

37.5 

208.6 

178.2 

11 

3330 

609.3 

104.6 

2390 

DATA   SERIES 

DATA    SERIES    I— Continued 


115 


No.  of 
16.2-foot 
Sections  to 
8  Inches 

Volume, 

Volume, 

D.B.H. 

Total 
Height 

Mer. 
Length  to 
8  Inches 

B.M.. 
16.2-foot 
Sections  to 
8  Inches 

Volume, 

Cubic  Feet 

(stem) 

Used 
Length 

B.M.  (a» 
cut  into 
logs  by 
logger) 

25.5 

188.6 

145.8 

9 

1440 

242.7 

70.1 

960 

23.5 

174.0 

145.8 

9 

1190 

197.2 

100.0 

890 

38.0 

215.4 

194.4 

12 

3670 

464.2 

162 . 0 

3240 

32.0 

183.9 

162.0 

10 

1820 

277.2 

109.0 

1280 

26.0 

147.1 

129.6 

8 

1070 

148.9 

94.2 

890 

32.4 

208.4 

178.2 

11 

2500 

378.8 

137.0 

2200 

29.0 

198.1 

162.0 

10 

1780 

298.6 

101.6 

1540 

34.5 

205.7 

178.2 

11 

2800 

424.2 

133.7 

2330 

34.6 

206.4 

178.2 

11 

2930 

369.8 

155.1 

2830 

29.0 

182.3 

129.6 

8 

1730 

246.9 

113.5 

1640 

27.5 

195.4 

162.0 

10 

1470 

210.9 

100.4 

1220 

17.2 

180.1 

113.4 

7 

570 

131.6 

72.9 

500 

41.3 

196.3 

178.2 

11 

3940 

542.8 

153.1 

3600 

29.2 

204.7 

158.0 

9f 

1680 

270.0 

147.5 

1550 

23.2 

187.9 

156.0 

9i 

1130 

189.6 

145.5 

950 

31.0 

204.5 

178.2 

11 

1950 

346.4 

148.3 

1850 

26.0 

186.9 

145.8 

9 

910 

170.9 

145.3 

880 

24.2 

151.6 

113.4 

7 

900 

132.2 

99.4 

810 

15.0 

125.0 

81.0 

5 

270 

47.4 

67.9 

230 

15.6 

137.8 

81.0 

5 

340 

73.3 

60.0 

230 

41.2 

241.0 

194.4 

12 

4610 

688.9 

186.6 

4360 

18.0 

157.7 

97.2 

6 

420 

87.5 

89.2 

340 

36.5 

210.6 

162.0 

10 

3940 

446.3 

117.6 

2510 

31.0 

194.3 

162.0 

10 

1660 

292.3 

142.1 

1490 

33.0 

199.3 

178.2 

11 

2040 

320.7 

98.6 

1500 

37.3 

226.5 

178.2 

11 

3180 

466.2 

151.3 

2820 

32.3 

190.9 

162.0 

10 

2110 

269.6 

123.4 

1760 

47.2 

229.8 

210.6 

13 

5810 

699.2 

167.8 

5110 

31.9 

225.2 

178.2 

11 

1910 

299.5 

162.3 

1830 

24.8 

184.9 

145.8 

9 

1340 

167.5 

103.0 

1080 

25.0 

193.2 

162.0 

10 

1360 

187.0 

97.4 

860 

34.0 

222.9 

194.4 

12 

3700 

428.8 

131.9 

2710 

31.0 

203.6 

162.0 

10 

1990 

294.2 

66.0 

1000 

37.8 

211.0 

194.4 

12 

4250 

589.6 

154.9 

4000 

35.2 

195.0 

178.2 

11 

3240 

464.6 

131.0 

3120 

38.5 

209.2 

162.0 

10 

2920 

331.4 

133.3 

2720 

34.0 

205.0 

178.2 

11 

2590 

413.5 

120.1 

2140 

32.0 

205.0 

178.2 

11 

2890 

360.0 

135.6 

2050 

17.0 

130.5 

97.2 

6 

490 

88.5 

96.0 

360 

40.0 

189.8 

45.8 

9 

2930 

455.4 

67.8 

2060 

31.5 

195.0 

162.0 

10 

1980 

332.6 

65.0 

1210 

29.5 

166.4 

129.6 

8 

1310 

224.9 

60.8 

890 

36.1 

193.2 

162.0 

10 

2830 

422.4 

114.8 

2240 

19.8 

150.1 

113.4 

7 

660 

116.3 

101.9 

590 

40.0 

195.0 

178.2 

11 

2900 

569.0 

66.5 

2470 

116 


APPENDIX 

DATA   SERIES    I— Continued 


No.  of 
l().2-foot 
Sections  to 
8  Inches 

Volume, 

Volume, 

D.B.H. 

Total 
Height 

iMor. 
Length  to 
8  inches 

H.M., 

16.2-foot 
Sections  to 
8  Inches 

V'olunie, 
Cubic  Feet 

(stem) 

Used 
Length 

B.AL  (as 

cut  into 

.  logs  by 

logger) 

50.0 

233 . 5 

210.2 

13 

7310 

703.9 

130.0 

5900 

26.0 

176.4 

145 . 8 

9 

1310 

238.6 

112.0 

1140 

32.0 

196.5 

162.0 

10 

2540 

376.1 

136.0 

2340 

25.0 

151.3 

145.8 

9 

1190 

158.4 

108.2 

790 

39.5 

224.9 

176.2 

11 

3970 

623.4 

129.9 

3010 

29.7 

194.0 

162.0 

10 

2170 

340.2 

103.0 

1720 

39.0 

206 . 5 

176.2 

11 

3980 

577.4 

110.0 

3590 

20.9 

190.0 

145.8 

9 

850 

150.8 

129.6 

790 

18.9 

118.4 

81.0 

5 

450 

85.6 

64.8 

360 

14.8 

107.0 

56.8 

3^ 

200 

53.3 

15.4 

102.0 

64.8 

4 

270 

57.5 

14.8 

95.5 

60.8 

3f 

210 

46.5 

14.7 

104.0 

62.8 

4 

230 

50.3 

13.0 

91.0 

48.6 

3 

160 

36.1 

14.5 

90.0 

46.6 

3^ 

150 

36.3 

13.2 

103.0 

52.8 

3i 

140 

38.1 

11.6 

95.0 

40.6 

2h 

80 

28.1 

15.7 

99.5 

60.8 

3| 

220 

51.1 

16.0 

104.0 

64.8 

4 

270 

59.3 

13.6 

102.0 

50.8 

3i 

110 

40.3 

13.6 

99.0 

52.8 

3i 

140 

39.3 

14.0 

90.0 

46.6 

3 

150 

35.4 

11.6 

92.0 

38.6 

2^ 

70 

28.2 

13.8 

87.0 

46.4 

3 

150 

35.8 

13.5 

92.0 

48.6 

3 

130 

34.8 

11.5 

94.0 

42.6 

2f 

80 

28.3 

11.6 

86.0 

40.6 

2h 

80 

26.4 

16.2 

117.0 

64.8 

4 

310 

71.7 

14.0 

94.0 

54.8 

4 

180 

44.7, 

13.6 

95.0 

54 . 6 

4 

150 

41.1 

11.2 

69.0 

16.2 

1 

40 

17.9 

13.6 

108.0 

58.8 

3i 

180 

44.8 

13.5 

85.5 

42.6 

3! 

130 

32 . 5 

12.0 

93.0 

48.6 

3 

150 

33.4 

11.2 

90.0 

40.6 

2h 

90 

28.9 

12.4 

95.0 

48.6 

3 

160 

38.1 

11.7 

83.0 

42.6 

2f 

110 

26.4 

12.1 

106.6 

28.6 

n 

160 

38.4 

13.0 

80.0 

48.6 

3 

150 

28.4 

15.8 

102.0 

69.8 

3f 

210 

51.6 

15.8 

97.0 

71.0 

4^ 

230 

68.1 

16.6 

104.0 

64.8 

4 

270 

58.2 

14.3 

114.0 

56.8 

31 

200 

49.9 

15.2 

96.0 

54.8 

3| 

170 

44.1 

14.3 

122.0 

56.8 

31 

200 

47.2 

DATA  SERIES 


117 


DATA    SERIES    I — Continued 


Volume, 

Volume, 

Mer. 

No.  of 

B.M.,      i 

Volume, 

B.M.  (as 

D.B.H. 

Total 
Height 

Length  to 

8  Inches 

i 
1 

16.2-foot 
Sections  to 
S  Inches 

16.2-foot 
Sections  to 
8  Inches 

Cubic  Feet 

(stem) 

1 

Used 
Length 

cut  into 
logs  by 

logger) 

16.0 

135 . 3 

91.2     i 

5! 

410 

77.8 

15.2 

147.9 

93.2 

51 

400 

82.9 

10  G 

85.0 

38.6 

2^        1 

80 

24.9     1 

11. G 

94.0 

42.6 

21 

110 

29.7      1 

.     13.8 

136 . 5 

81.0 

5 

320 

66.4      1 

14.5      1 

84.0 

42.6 

21 

110 

34.0 

12.0 

73.5 

32.4 

2 

90 

24.0 

15.8 

102.0 

60.8 

31 

210 

51.6 

14.9       i 

117.0 

64.8 

4 

270 

57.6 

11.0      ! 

90.0 

40.6 

2h 

90 

27.2 

11.6 

94.0 

42.6 

21 

110 

29.7 

11.1 

83.0 

38.6 

2i 

70 

23.0 

11.6 

87.0 

46.6    ; 

3 

120 

28.7 

17.0 

145.0     ' 

97.2 

6 

410 

82.3 

16.0 

136.0 

91.2 

51 

360 

73.0 

18.0 

133.0 

97.2 

6 

450 

89.3 

17.8 

132.0 

97.2 

6 

460 

86.1 

16.5 

142.0 

95.2 

6 

370 

79.2 

21.4 

162.0 

127.6 

8 

860 

145 . 8 

23.5 

167.0 

121.6 

7^ 

1030 

186.8 

21.0 

152 . 0 

107.4 

61 

680 

126.4 

20.0 

152.0 

113.4 

7 

630 

120 . 1 

21.0 

159.0 

107.4 

6i 

650 

129.8 

17 . 5 

157 . 0 

97.2 

6 

450 

94.5 

23.5 

170.0 

129.6 

8 

1230 

207  . 5 

22.2 

130.0 

109.4 

61 

670 

132.5 

19.0 

140.0 

97.2 

6 

530 

1        116.9 

19.8 

152.0 

107.4 

6| 

680 

123.6 

18.6 

137.0 

113.4 

7 

1          580 

96.9 

19.2 

152.0 

1        107.4 

6f 

,          490 

1          99.8 

20.0 

'        159.0 

113.4 

7 

760 

1        140.0 

17.5 

1        122.0 

81.0 

5 

400 

76.5 

17.7 

138.0 

97.2 

'            6 

570 

99.3 

17.1 

147.0 

91.2 

H 

440 

i          86.2 

19.0 

148.0 

111.2 

7 

660 

115.9 

18.8 

i        144 . 0 

97.2 

6 

490 

99.6 

31.7 

174.0 

145.8 

9 

1940 

301.1 

26.0 

182.0 

141.8 

SI 

1300 

212.4 

26.2 

161.0 

135.8 

81 

1300 

195.2 

22.6 

162 . 0 

129 . 6 

8 

890 

144.9 

25.0 

171.0 

129.6 

8 

1600 

255.3 

27.0 

156.0 

111.4 

7 

690 

153.1 

33.4 

207.0 

176.2 

11 

3300 

477 . 3 

33 . 5 

210.0 

176.2 

11 

3490 

487.6     ' 

21.7 

183.7 

1 

145.8 

9 

950 

167.8     1 

118 


APPENDIX 

DATA   SERIES    I— Continued 


No   of 

Volume, 

Volume, 

D.B.H. 

Total 
Height 

Mer. 
Length  to 
8  Inches 

16.2-foot      ,f;,," 
c     ,.         ,       16.2-foot 
Sections  to   „       . 

8  Inches      ««^tions  to 

Volume, 

Cubic  Feel 

(stem) 

Used 
Length 

B.M.  (as 
cut  into 
logs  by 

8  Inches 

logger) 

19.2 

138.2 

113.4 

7 

690 

102.5 

22.8 

178.6 

129.6 

8 

910 

164.6 

21.6 

176.6 

139.8 

8^ 

1040 

169.1 

31.5 

199.5 

162.0 

10 

1980 

311.8 

24.5 

190.8 

143.8 

9 

1260 

219.2 

24.3 

210.2 

160.2 

10 

1620 

263.0 

24.4 

183.0 

145.8 

9 

1230 

208.2 

36.1 

197.6 

160.2 

10 

2670 

426.9 

36.0 

204.2 

174.2 

10^ 

2810 

430.4 

32.5 

206.8 

174.2 

m 

2580 

401.3 

33.9 

207.0 

162.0 

10 

2720 

443.1 

24.7 

192.0 

143.8 

9 

1400 

233.4 

34.2 

200.6 

162.0 

10 

2620 

395.9 

27.5 

202.2 

143.8 

9 

1530 

265.0 

17.8 

165.0 

97.9 

6 

420 

86.8 

27.5 

202.2 

143.8 

9 

1530 

264.9 

11.7 

83.0 

42.6 

2i 

110 

26.4 

13.5 

85.5 

43.6 

21 

130 

35.8 

16.5 

117.0 

72.8 

4^ 

340 

70.6 

15.5 

112.0 

64.8 

4 

280 

59.4 

19.5 

135.0 

97.2 

6 

1610 

110.6 

20.0 

149.1 

97.2 

6 

660 

126.2 

27.0 

161.2 

123.6 

7i 

1410 

224.8 

16.0 

136.7 

91.2 

5- 

360 

74.2 

16.3 

126.2 

81.0 

5 

460 

89.4 

15.6 

136.3 

93.2 

H 

360 

75.7 

16.0 

136.8 

81.0 

5 

340 

75.0 

15.6 

136.9 

97.2 

6 

440 

83.9 

13.9 

116.8 

60.8 

3f 

190 

47.5 

12.9 

127.4 

56.8 

3^ 

150 

39.7 

14.1 

130.2 

75.0 

4f 

270 

59.8 

14.5 

137.2 

91.2 

5f 

360 

71.9 

27.0 

184.6 

162.0 

10 

1780 

288.6 

31.5 

206.2 

176.2 

11 

2730 

404.1 

27.6 

207.8 

129.6 

8 

1460 

305.2 

20.3 

188.8 

143.8 

9 

1020 

177.3 

21.2 

158.0 

113.4 

7 

620 

118.9 

30.2 

180.0 

111.4 

7 

1310 

244.6 

21.4 

160,0 

125.6 

7-J- 

800 

144.9 

•  38.2 

209 . 9 

174.2 

10  J 

3870 

559 . 2 

25.0 

191.3 

160.0 

10 

1 3S() 

240.6 

25.0 

176.0 

145.  S 

9 

1590 

236.2 

25.9 

ISO.  6 

145.8 

9 

1540 

218.3 

41.6 

200.0 

129.6 

8 

3330 

528.3 

30.0 

201.5 

162.0 

10 

1730 

286.9 

DAI. A   SERIES 


119 


DATA    SERIES    I — Continued 


No.  of 
16.2-foot 
Sections  to 
8  Inches 

Volume, 

Volume, 

D.B.H. 

Total 
Height 

Mer. 
Length  to 
8  Inches 

B.M., 
16.2-foot 
Sections  to 
8  Inches 

Volume, 
Cubic  Feet 

(stem) 

Used 
Length 

B.M.  (as 
cut  into 
logs  by 
logger) 

18.9 

162.0 

113.4 

7 

600 

116.0 

17.8 

151.3 

107.4 

6| 

470 

93.8 

19.7 

162.0 

117.6 

7i 

770 

132 . 1 

17.8 

165.0 

97.2 

6 

420 

86.8 

;12.5 

185 . 8 

162.0 

10 

2510 

360.9 

38.5 

211.5 

162.0 

10 

3180 

471.4 

34.4 

217.0 

162.0 

10 

3010 

480.7 

26.8 

160.0 

111.4 

7 

930 

176.6 

26.5 

200.6 

162.0 

10 

1840 

299.2 

28.1 

196.0 

162.0 

10 

1960 

323.7 

22.2 

157.5 

129.6 

8 

1010 

161.0 

41.0 

204.0 

139.8 

81 

3150 

488.9 

27.7 

160.2 

106.9 

960 

27.8 

171.1 



123.1 

1250 

30.5 

149.2 

101.0 

1120 

33.9 

171.7 

114.3 

1120 

34.0 

168.8 

129.8 

1560 

35.0 

182.0 

99.0 

1830 

37.0 

167.0 

114.0 

1940 

37.2 

176.9 

133.4 

2360 

38.1 

178.0 

• 

111.0 

2700 

16.3 

118.2 



70.4 

260 

16.5 

109.3 

66.8 

260 

18.2 

138.4 

70.4 

300 

22.0 

135.3 

64.5 

460 

22.4 

169.8 

101.8 

560 

58.0 

226.6 



158.8 

6280 

53.5 

219.7 

153.5 

7660 

18.3 

126.5 



65.3 

290 

22.5 

132.5 



72.7 

600 

49.0 

258.6 

154.2 

4890 

57.1 

255 . 2 

1 

164.4 

4820 

60.0 

213.5 

. 

161.5 

8170 

57.0 

205.5 



128.0 

6440 

20.0 

121.5 

58.2 

270 

18.0 

129.5 

108.0 

320 

47.1 

179.3 



167.6 

5070 

30.5 

182.0 

1 

149.2 

1670 

47.0 

210.6 



148.0 

4580 

39.0 

189.3 



114.5 

2490 

36.0 

193.2 

117.0 

2510 

52.2 

202.4 

111.7 

4490 

30.1 

200.0 

139.0 

1570 

43.5 

230.0 

1      

121.7 

3440 

41.8 

184.8 

1  



i 

131.6 

2510 

120 

APPENDIX 

DATA   SERIES   1— Continued 

No.  of 

Volume, 

Volume, 

Mer. 

B.M., 

Volume, 

B.M.  (as 

D.B.H. 

Total 
Height 

Length  to 
8  inches 

16.2-foot 
Sections  to 
8  Inches 

16.2-foot 
Sections  to 
8  Inches 

Cubic  Feet 
(stem) 

Used 
Length 

cut  into 
logs  by 
logger) 

22.0 

175.1 

102.6 

750 

42.2 

199.5 

122.1 

3310 

47.0 

202.3 

134.5 

6240 

44.6 

237.9 

134.3 

3080 

42.4 

214.6 

135.1 

3130 

48.5 

244.0 

145.1 

4030 

45.5 

221.2 

122.6 

3760 

41.0 

194.2 

135.1 

3290 

42.2 

182.5 

101.8 

2820 

52.3 

229.8 

125.3 

3980 

48.4 

212.9 

130.9 

3180 

45.4 

208.2 

127.0 

3350 

42.5 

216.3 

156.6 

4280 

30.5 

189.6 

124.0 

1510 

35.7 

187.2 

127.8 

2290 

54.0 

239.8 

179.2 

6770 

59.7 

175.6 

6140 

40.0 

148.9 

3870 

52.2 

186.7 

8490 

60.5 

141.8 

8150 

45.5 

179.6 

4451 

47.0 

138.4 

6050 

54.0 

136.4 

5490 

52.0 

112.6 

5500 

53.0 

151.6 

6890 

49.5 

151.6 

5690 

48.0 

192.6 

4270 

48.0 

130.8 

3510 

49.0 

147.3 

5090 

54.0 

195.2 

7130 

49.0 

142.5 

5850 

52.0 

153.8 

7140 

48.0 

154.9 

3820 

46.0 

112.1 

3640 

38.0 

155.8 

2410 

44.0 

144.4 

4310 

44.0 

154.2 

4640 

41.0 

124.3 

3610 

52.0 

176.8 

8930 

46.0 



172.1 

6130 

46.0 

156.3 

4760 

60.0 

155.6 

8580 

DATA  SERIES 


121 


DATA   SERIES    II 
Measurements  of  Periodic  Growth  at  the  Stump 
Collected  in  Pure  Western  Yellow  Pine  Stands  at  Manitou  Park,  Colo. 


Periodic 

Periodic 

Periodic 

Tree 

D.B.H., 

Growth, 

Tree 

D.B.H., 

Growth, 

Tree 

D.B.H., 

Growth, 

No. 

Inches 

Inches  * 
(Radius) 

No. 

j 

Inches 

Inches  * 
(Radius) 

No. 

Inches 

Inches  * 
(Radius) 

1 

U.O 

0.20 

!         IS 

11.0 

0.40 

37 

11.0 

0.60 

2 

9.5 

0.30 

19 

9.0 

0.55 

38 

13.0 

0 .  50 

3 

6.0 

0.55 

1      21 

13.0 

0.20 

39 

9.0 

0.60 

4 

13.5 

0.30        , 

'      22 

11.5 

0.40 

40 

10.0 

0.50 

5 

17.0 

0.20 

24 

5.2 

0.55 

42 

7.0 

0.55 

6 

10.6 

0.25 

!      25 

8.0 

0.50 

44 

6.5 

0.50 

8 

10.0 

0.45 

26 

9.0 

0.40        1 

45 

6.5 

0.60 

9 

11.0 

0.40 

1      27 

18.0 

0.25 

46 

9.1 

0.50 

10 

18.0 

0.30 

29 

11.0 

0.40 

47 

7.5 

0.60 

11 

16.0 

0.30 

<      30 

10.2 

0.45 

48 

9.1 

0.30 

12 

18.0 

0.30 

31 

12.5 

0.40 

49 

10.0 

0.35 

15 

12.0 

0.30 

33 

16.0 

0.30 

50 

11.5 

0.40 

16 

7.0 

0.50 

34 

10.5 

0.85 

51 

18.0 

0.20 

17 

12.5 

0.35 

36 

11.2 

0.50 

52 

5.9 

0.60 

Measurements  represent  outermost  ten  rings  on  average  radius. 


122 


APPENDIX 


CO 

% 

o 

Q 

t 

c 

I 

a 

1 

CO 

3 
03 

Pi 

1 

<; 

c 
o 

c 

s 

■* 

^           00           OOSrHOOCCiO           iOT»i                          (n'm'th' 

CO 

OOCOCCt^t^i#iM0500^»oSt-(MQ005iMCCi2           O 

-*^^XC0005^C<C2iO(M-*fOiM(NC^(N(N^           O 

c^ 

tO    "O    iC 

00OCT>O'O>0C^G0(Nf0'*'-lO-*'-HiOt^00O00<MO 

2    O    CO    00    00    O    0__0    C^M^(MTj<CO(N(N(N^(NO<Na> 

- 

>0                                         lO           >0                   lO    iC 
(N(Mt^>OCCi-<<GOCOt^l^t^t^CO>.O0OC^— iMt^-rHOiCC 

CCOiMt^QOOQOO^^COi-icOiM^'M'M'-i^O^O 

o 

CDt^rHCOiM(N-^OOOi-it^CO<r>01'*<050a>COO<NO 

CJ05(Nt^00O00a>'H^C^,-((M,.HrH,-i^O'-'O'-<Ci 

05 

iX)iM.-iC^Ot^OCO'M:000000>iOCSCO-*,-iOiOOt>. 

-HOr-it^OOOOOOlOOrHO-H^O^OOr^OOOO 

00 

ict-c«ioo5<Not-oooQOooo^coor-Tt*.OQOt^u:i 

oooot^t-cr-t^oooiOJ005'-Hr-iO'-«050iOooo5oo 

t^ 

'*<^-*0--D'sDO^^C5'000<OQO^OiOt^CO^M 

0iXO5Ot^X^C000Q0O503OOO5OOQ005000>00 

o 

■^CCXlMOO^-^t^OfOINOO^O^C^CD^rHMt- 

OOt-00?D1^000t^t^OOOOOOOOOCT>0500t^05t>-OOl> 

•o 

t^Tt<00cD-O<MO00O-^CC(M«0>0O0iC0l:^iM05O(N 

t^COt^'OOt^iOOt^t^t^t^t^OiaON.l^OOO'-Dt^I^ 

•* 

05CCI>OOiM'-i05'-Hl:^(NCCiNOOOCDr(HiCeCCOOOOOOO-«*< 

0»OCO»OCOCOiCiOOO«0?OCDOOt^incO»Ot^CO;DO'^iOCO 

M 

00i-ll~-O-*(NCCi0>'-i0;00(N'-<t>-»-<(Ni-H-*(N-*00t^t>-'-Hi-t 

»0'*iO-':t<»0'OTf<T}<iOiO'<l*»CiOt>.0»«»OT}<«OiOiO»CCO-^iM 

IN 

eOQOO-^j^ost^^co^cci^ocoooi^TiHiNosOosoooiocnoo 

-*(MTj<(NCCCOCCCOCCTj*(N-<l<eC»OT)4M«)(N-*eC-*CO(N(NO 

- 

Oe0eC'*i0i0i-HOt^(NTt<000ii0C0<N?0iM0005O^t^'-'O 

C^O(NO.-irHrH^O^O.-HO(MM'-H^Opp<N^O^O 

1 

<5 

.-iO>Ct^.-i.-iOO'-iOC»<N05eQ-<l<»0iCO05a>«0<N00(NO 

D.B.H. 

'-lOlMOC^OON.OOOiOOOtOiCiCOiOiOiCO-^C^OOOOl 

^^^^^n^'c^^^^^^U^^^^^'ci^^^^^'- 

6 

.-<(NCO-*iOCOt^00050^(NCO't-iOCOt^OOC50^(NCO^":> 

DATA   SERIES  123 


(M    t^    t-    •^ 


O    >-0    05    GO 
(N    O    O    CC 


lO    05    t»    ^ 
IM    ■>*    iC    CO 


Tj<    (N    CO    <N 
(N    Tt*    Tt<    C<1 


iM    O    CO    CO 

IN     eC     CC     rH 


CD    1^    CO    00 
--<    r-1    (N    d 


0(NOt^'-i  00»-<COCOi-'5 

i-hO^OSOO  CO0Ot-t~-t>- 


lO  'O  '^ 

r^iOOCOt^05l^>*'-'<M  t-C0^^C0(N(NO(NC005CC-*0iNt-'*00i0 

i>!co-*»0'*co-*iocooo       TjJcDoioJxt^ojcot^cdcdt^r^r^OQOio-^oi 


eCO>»COOOCDCDOCO'-H<-H>OCOCOCOOCOOOGO(N(>lO'*(NOOr>-COCD^0505"^0 
CO  t-'  N^  t^;  CO  i-O  CO  lO  r*;  CO  tT  'I''  O  t-^  CO  ^'  ci  t-^  t-  OC  CO  00  iC  CO  CD  d  CO  CD  CO  lO  I>  ■*■  T}<  00 


coOQOMCi^t--Hcot-^t-ooo»ocoocco-H-;co>ococoi>.'OcoMO>oco<NOeo 

O     CD     O     CO     >0     Tji     C^"     Tt-'     Tf'     Tt;     CO     CO     ^'     U'^     CS     ^"     b-'     CO     CO     ^^     ^     CO     TjJ     Tli     Tt*     Tl<     O     »0     Tl<     Tt<     CO     ^     Tt<     CO 


Tji-*St-COCD^OiOCDC^t-T«OQOU:OOC50>"5Mt-.eO^COC^CDQ005t-.»COOO 
eO   CO    CO    CO    CO    (N    ^    C^'    CO    d    M    N    CO    Tfi    -h'    CO    CD    lO    CO    Tf'    d    ^'    C^'    ^1    CO    C^    CO    CO    c^ 


OlQO(N'-<COCO<NC005«Oa)0»CO'HC5COiOTj<,-.COCOTtHCO»OCOCOC>^Tj<U^iO,--;cOOJ 


^5g5g§SS:sg§§SSJ?;S§gg5S§J?5J^i^SS;§i^:SSSSS 


005MO^'*'HOO'*t-COOO(NOOO^OOcOiOcD050-<^^Tl<(Nt-iOOTt<<NiO 

d^'^"^d;cdcod;2d«2;^'^2^^':^?o2§2^2222§22^2N 


§^g§g;;????^J?^^^^55:^5^^^^^53sssss§!^s§ 


124 


APPENDIX 


DATA    SEKIES    IV 

Height  Growth    Mkasuhements 

Collected  in  Pure,  Even-aged,  Second-growth  Stands  of  Douglas  Fir  in  Western  Washington 

on  Site  Quality  1 

(Average  stump  height  2  feet) 


Total 

Age, 

Years 

Total 

Height, 

Feet 

Number  Rings  at  Various  Height  Above  the  Gro 

und 

Tree 
No. 

No. 

Height 
Above 

No. 

Height 
Above 

No. 

Height 
Above 

Rings 

Ground, 
Feet 

Rings 

Ground, 
Feet 

Rings 

Ground, 
Feet 

1 

55 

111.0 

43 

16 

2 

39 

93.0 

20 

47 

3 

40 

117.0 

22 

45 

4 

55 

111.0 

49 

14 

5 

53 

111.0 

48 

14 

6 

39 

106.0 

22 

44.5 

7 

48 

124.0 

43 

16 

8 

131 

192.2 

118 

37 

109 

70 

9 

136 

176.0 

122 

34 

106 

74 

10 

135 

190.8 

118 

36.0 

63 

157.0 

11 

137 

162.0 

114 

35.0 

86 

110.0 

12 

131 

138.2 

119 

27.0 

97 

75.0 

77 

118.0 

14 

140 

191.3 

114 

44.0 

68 

140.0 

16 

140 

184.6 

116 

48.0 

105 

83.0 

54 

157.6 

17 

132 

160.0 

114 

43.0 

97 

118.0 

20 

134 

210.2 

109 

68.0 

84 

133.0 

21 

135 

212.6 

111 

52.0 

80 

131.0 

22 

136 

202.2 

121 

36.0 

103 

85.0 

78 

144.0 

25 

139 

180.6 

82 

130.0 

26 

140 

183.7 

115 

51.5 

27 

135 

210.5 

82 

128.5 

DATA   SERIES 


125 


DATA   SERIES  V 

Complete  Stem  Analysis.     SPECIES,  Western  Yellow  Pine 
LOCALITY,  Manitou  Park,  Colo. 


Regular  Volume  Measurements 

As  Used  by  Logger 

1 

c 

o 

1 

en 
< 

r 

Q 

is 

ft 

1 
-S 

G 

Volume 

J! 

-1 

> 

239 
166 
151 

2.0 
16.0 
16.0 
26.0 

16.8 
15.6 
12.8 

0.8 
0.5 

18.4 
16.6 

1 
St. 

2 

3 

Top 

i 

4 

5 

6 

7 

8 

9 

10 

...... 

11 

12 

13 

14 

15 

1 

1 

16 



1 

17 

18 



' 

19 

1 

1 

1 

1 

rree  No.  67 

SUMMARY 

Plot  No 

0 

1* 

No.  of 
Logs 

Volume, 
Cubic; 
Feet 

Volume, 
B.M. 

si 

is 

> 

245 

60 

1 

18 

18. U 

\ 

' 

Name,  F.  H.  Rice. 


Date,  7,  17,  '09. 


126 


APPENDIX 


DATA   SERIES 

DATA   SERIES    Y—Continued 


12' 


Regular  Volume  Measurements 

As  Used  by  Logger 

c 
.2 

1 

i 

15.0 

13.8 

10.0 

6.6 

■5^ 

CD 

Q 

Volume 

g^ 

> 

1 

204 
192 
163 
94 

2.7 
16.0 
16.0 
16.0 
12.4 

0.60 
0.35 
0.25 
0.20 

16.2 

14.5 

10.5 

7.0 

St. 
2 

S 

4 

f> 

Top 

6 

7 

8 

q 

10 

n 

1"? 

13 

14 

15 

16 

17 

18 

IQ 

?0 

Tree  No.  IK 


SUMMARY 


Plot  No. 


_    01 

"5 

> 

Volume, 
B.M. 

is 

> 

16 

212 

63.1 





22  7 

Name,  F.  P.  McKown. 


Date,  7,  17.  "09. 


128 


APPENDIX 


00 

o 

o 

»o 

tN. 

§ 

§ 

lO 

iO 

o 

o 

s 

lO 

"O 

lO 

s 

g 

.0 

■^ 

•rf' 

§ 

§ 

-* 

■<*< 

•«}< 

^: 

g 

^ 

■* 

-* 

c^i      CO      CO      CO 


M        CO        (N        IM 

0000 

CO     00      o      o 

ci        (N       C^        (N 


O  ^  .-H 


j. 

CO 

- 

0 

CO 

CO 

CO 

CO 
CO 

CO 

^ 

^ 

0 

00 

'X) 

•0 

^ 

CO 

C4 

(N 

g 
t^ 

g 

1    ^ 

5 

DATA   SERIES 


129 


DATA   SERIES    V— Continued 


Regular  Volume  Measurements 

As  Used  by  Logger 

• 

c 
.2 

1 

< 

£^ 

1.6 
16.0 
16.0 

4.0 

is 

Volume 

¥ 

> 

1 

104 
67 
25 

9.4 
6.8 
2.0 

0.6 
0.3 
0.1 

10.2 
7.4 
2.2 

St. 
2 

3 

4 

Top 

5 

... 

6 



7 

8 

9 

10 

11 

1? 

13 

14 

15 

16 

17 

18 

19 

?.o 

Tree  No.  IS 


SUMMARY 


Plot  No. 


^ 

JZ 

^ 

H 

-5  si 

a 

-og 

III 

Volume, 
B.M. 

•Ul 

3 

73   (U 

H 

6^ 

> 

10 

109 

37.6 

> 


Name,  O.  .1.  Staunchfieid. 


Date,  7,  19,  '09. 


130 


APPENDIX 


—I      «      c^ 
odd 


CO      CO 


>o     o 

CO         05 
C^        IN 


QCO 


t>.       00       O       O 


DATA   8EKIES 


131 


DATA   SERIES    VI 
Statistics  of  Sample  Acre  Plots  in  Pure  Even-aged  Stands  of  Douglas  Fir 
Data  collected  by  the  U.  S.  Forest  Service,  1909  and  1911,  in  Western  Washington  and 


Oregon. 


SITE   QUALITY    I 


Location  and  Plot  Number 


Saddle  Mt.,  Siuslaw,  N.F. 

96 

95 

97 

89; 

94 

88 

91 

Cougar  Cr.,  Ore. 

44 

49 

48 

58 

55 

62 

Bacon  Creek,  Washington,  N.  F. 

167 

160 

163 

149 

161 

165 

Parmelia  Trail,  Santiam,  N.  F. 

125 

129 

139 

138 

137 

136 

Lucia,  Wash. 

7 

1 

5 

504 

510 

502 


No.  of 
Trees 

Stand. 
Years 

Volume 

Basal 

Area, 

Square 

Feet 

Cubic 
Feet 

Feet, 
B.M. 

208 

38 

4,704 

15,604 

131 

347 

38 

6,327 

19,920 

179 

231 

38 

5,285 

17,878 

148 

263 

38 

6,813 

23,847 

190 

386 

38 

7,288 

20,514 

195 

186 

38 

6,306 

25,263 

172 

252 

38 

7,022 

24,397 

194 

367 

51 

7,266 

17,481 

179 

262 

51 

9,888 

35,766 

227 

286 

51 

9,668 

30,036 

206 

547 

51 

9,818 

14,389 

254 

347 

51 

9,192 

28,305 

218 

373 

51 

9,253 

22,675 

211 

265 

62 

8,119 

28,779 

185 

233 

62 

11,725 

49,757 

261 

302 

62 

12,073 

45,097 

271 

241 

62 

11,469 

48,012 

255 

186 

62 

10,740 

47,816 

238 

182 

62 

10.139 

43,030 

217 

260 

107 

18,324 

103,134 

368 

228 

107 

20,500 

120,096 

394 

177 

107 

19,168 

111,741 

366 

219 

107 

18,709 

102,64 

363 

216 

107 

19.421 

113,284 

370 

176 

107 

22,589 

140.570 

432 

84 

121 

19,021 

108,860 

342 

70 

121 

14,429 

79,250 

263 

95 

121 

25,560 

154,517 

458 

93 

121 

24,047 

141,234 

431 

72 

121 

16,476 

95,458 

296 

67 

121 

18,841 

112,992 

337 

1 

D.B.H. 

of 

Average 

Tree, 

Inches 


10.7 
9.8 
10.8 
11.5 
11.2 
10.5 
11.9 

9.5 
12.6 
11.5 

9.2 
10.7 
10.2 

11.3 
14.3 
13.8 
13.9 
15.3 
14.8 

16.1 
17.8 
19.5 
17.4 
17.7 
21.2 

27.3 
26.2 
29.7 
29.1 
27.4 
30.3 


Height 

of 

Average 

Tree, 

Feet 


88 
85 
88 
91 
89 
87 
92 

95 
110 
105 

93 
101 

98 

108 
117 
115 
116 
120 
118 

135 
141 
148 
140 
141 
155 

173 
169 
178 
177 
173 
180 


*  This  table  includes  all  species  on  the  acre  plot  except  cedar.  The  latter  is  considered 
an  understory.  Douglas  fir  is  the  predominating  soecies,  with  scattering  hemlock,  firs,  spruce, 
pines  and  hardwoods.     All  trees  to  2  inches  D.B.H.  are  tallied  by  inch  classes. 

Board  measure  based  on  trees  12  inches  and  over  in  diameter. 


132 


APPENDIX 


DATA   SERIES   \I~iContinued) 
Statistics  of  Sample  Acre  Plots  in  Pure  Even-aged  Stands  of  Douglas  Fir 
Data  collected  by  the  U.  S.  Forest  Service,  1909  and  1911,  in  Western  Washington  and 
Oregon.* 

SITE  QUALITY   II 


No.  of 
Trees 

Stand, 
Years 

Volume 

Basal 

Area, 

Square 

Feet 

D.B.H. 

of 
Average 

Tree, 
Inches 

Height 

Average 
Tree, 
Feet 

Location  and  Plot  Number 

Cubic 
Feet 

Feet, 
B.M. 

Marmot,  Ore. 

308                   

208 
257 
236 
235 
252 
184 
215 

254 
264 
222 

448 
400 
582 
412 

305 
212 
277 
295 
261 
228 
183 

250 
190 
269 
278 

50 
50 
50 

57 
57 
57 
57 

98 
98 
98 
98 
98 
98 
98 

119 
119 
119 
119 

6,101.5 
5,750.0 
4,979.0 
6,376.0 
6,373.0 
6,484 . 0 
6,433.0 

6,334.2 

7,108.8 
7,728.8 

6,747.8 
8,909 . 8 
8,674.8 
8,650.4 

10,380.0 
13,108.0 
12,970.0 
13,351.0 
12,327.0 
14,842.0 
12,482.0 

15,433.4 
14,879.5 
15,355.1 
14,764.6 

15,429 
15,476 
11,812 
19,485 
18,360 
21,953 
21,233 

19,442 
21,331 
29,277 

12,742 
27,894 
17,218 
25,750 

44,055 
64,428 
62,240 
61,142 
.'^7,640 
75,103 
65,699 

64,230 
68,608 
65,206 
64,302 

169.1 
159.0 
138.0 
172.0 
173.0 
170.0 
171.0 

156.06 
181.73 
195.43 

207.04 
255.15 
272.00 
249.08 

242.0 
292.0 
295.0 
304.0 
280.0 
333.0 
294.0 

319.54 
302.33 
330.45 
325.54 

12.2 
10.7 
10.3 
11.6 
11.2 
13.0 
12.0 

10.6 
11.3 
12.7 

9.2 
10.8 

9.3 
10.6 

12.0 
15.9 
14.0 
13.8 
14.0 
16.3 
17.1 

15.3 
17.1 
15.0 
14.6 

93 

307              

89 

306          

86 

305     

91 

304 

90 

303 

96 

302                               

92 

Morton,  Wash. 

262                            

93 

261                       

97 

260                   

103 

Huckleberry  Mt.,  Oregon  N.  F. 
293      

78 

292     

85 

291      

78 

290      

84 

Santiam  N.  F.,  Minto  Trail 

123 

102 

112 

119 

lis 

111 

117                               

110 

116                          

111 

114              

120 

122              

123 

Columbia  N.  F.  Racetrack  Trail 
21               

127 

22          

132 

23      

126 

24 

125 

*  This  table  includes  all  species  on  the  acre  plot  except  cedar.  The  latter  is  considered 
an  understory.  Douglas  fir  is  the  predominating  soecies,  with  scattering  hemlock,  firs,  spruce, 
pines  and  hardwoods.     All  trees  to  2  inches  D.B.H.  are  tallied  by  inch  classes. 

Board  measure  based  on  trees  12  inches  and  over  in  diameter. 


DATA  SERIES 


133 


DATA  SERIES   VI— (Con(mued) 
Statistics  of  Sample  Acre  Plots  in  Pure  Even-aged  Stands  of  Douglas  Fir 
Data  collected  by  the  U.  S.  Forest  Service,  1909  and  1911,  in  Western  Washington  and 
Oregon.* 

SITE   QUALITY   III 


Location  and  Plot  Number 


\f 

Volume 

Basal 
Area, 

D.B.H. 

of 

No.  of 

Trees 

Stand, 
Years 

Cubic 
Feet 

Feet, 
B.M. 

Square 
Feet 

Tree, 
Inches 

306 

57 

6,845.3 

20,383 

209.56 

11.2 

292 

57 

7,635.3 

25,630 

229.80 

11.9 

385 

57 

7,173.4 

15,017 

203.41 

9.9 

520 

57 

5,946.4 

8,065 

198.62 

8.3 

481 

57 

6,128.0 

9,005 

203.79 

8.8 

524 

57 

5,596.5 

7,502 

190.52 

8.1 

537 

57 

6,379.3 

7,268 

214.57 

8.6 

587 

57 

5,887.1 

4,719 

202.77 

8.9 

635 

57 

5,260.9 

3,169 

190.49 

7.4 

505 

57 

5,862.8 

8,452 

186.28 

8.2 

741 

57 

5,029.2 

3,311 

158.47 

6.2 

574 

58 

6,131.0 

11,346 

176.38 

7.5 

431 

58 

8,272.2 

22,558 

218.97 

9.7 

814 

58 

6,092.0 

8,984 

184.54 

6.2 

138 

70 

5,282.0 

21,201 

130.00 

13.1 

201 

70 

7.488.0 

30,127 

184.00 

13.0 

'  196 

70 

9,790.0 

42,071 

240.00 

14.3 

133 

97 

9,046.0 

37,032 

205.00 

16.8 

146 

97 

10,435.0 

42,160 

234.00 

17.7 

130 

97 

7,743.0 

34,137 

182.00 

16.0 

143 

97 

11,326.0 

45,555 

247.00 

17.8 

134 

97 

10,074.0 

41,064 

222 . 00 

17.4 

179 

97 

8,740.0 

29,935 

191.00 

14.0 

179 

97 

11,775.0 

47,922 

261.00 

13.1 

145 

97 

10,480.0 

42,210 

230.00 

17.0 

164 

97 

10,358.0 

41,108 

235.00 

16.2 

158 

120 

9,127.0 

44,507 

191.00 

14.9 

133 

120 

12,327.0 

64,703 

243 . 00 

18.3 

149 

120 

7,649.0 

31,596 

155.00 

13.8 

105 

120 

6,742.0 

35,762 

145.00 

15.9 

176 

120 

8,825.0 

45,524 

176.00 

13.6 

137 

120 

10,987.0 

53,522 

215.00 

16.9 

Humphrey,  Wash. 

235 

236 

237 

238 

239 

240 

241 

242 

243 

244 

246 

Morton,  Wash.,  Handle  Road 

253 

254 

255 

Columbia  N.  F.,  Racetrack  Trail 

2 

3 

6 

Columbia  N.  F.,  Huckleberry  Mt 

30 

29 

31 

32 

33 

38 

39 

40 

41 

Frank  Brice  Cr.,  Ore. 

145 

144 

135 

138 

137 

139      


*  This  table  includes  all  species  on  the  acre  plot  except  cedar.  The  latter  is  considered 
an  understory.  Douglas  fir  is  the  predominating  species,  with  scattering  hemlock,  firs,  spruce, 
pines  and  hardwoods.     All  trees  to  2  inches  D.B.H.  are  tallied  by  inch  classes. 


Board  measure  based  on  trees  12  imihes  and  over  in  diameter. 


FMPEH. 


